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19-1 | 2015 Logic and Philosophy of Science in Nancy (II) Selected Contributed Papers from the 14th International Congress of Logic, Methodology and Philosophy of Science

Pierre Édouard Bour, Gerhard Heinzmann, Wilfrid Hodges et Peter Schroeder-Heister (dir.)

Édition électronique URL : http://journals.openedition.org/philosophiascientiae/1027 DOI : 10.4000/philosophiascientiae.1027 ISSN : 1775-4283

Éditeur Éditions Kimé

Édition imprimée Date de publication : 1 mars 2015 ISBN : 978-2-84174-707-8 ISSN : 1281-2463

Référence électronique Pierre Édouard Bour, Gerhard Heinzmann, Wilfrid Hodges et Peter Schroeder-Heister (dir.), Philosophia Scientiæ, 19-1 | 2015, « Logic and Philosophy of Science in Nancy (II) » [En ligne], mis en ligne le 01 mars 2015, consulté le 06 novembre 2020. URL : http://journals.openedition.org/philosophiascientiae/ 1027 ; DOI : https://doi.org/10.4000/philosophiascientiae.1027

Ce document a été généré automatiquement le 6 novembre 2020.

This issue collects a selection of contributed papers presented at the 14th International Congress of Logic, Methodology and Philosophy of Science in Nancy, July 2011. These papers were originally presented within two of the main sections of the Congress. They deal with general philosophy of science (including ethical and historical aspects of philosophy of science), and philosophy of biology, physics, chemistry and economics. A first volume of contributed papers, dedicated to logic, philosophy of mathematics and cognitive science, and philosophy of technology, appeared in the last issue of Philosophia Scientiæ (18-3), 2014.

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SOMMAIRE

Logic and Philosophy of Science in Nancy (II)

Preface Pierre Edouard Bour, Gerhard Heinzmann, Wilfrid Hodges et Peter Schroeder-Heister

A New Role for Data in the Philosophy of Science Molly Kao

From Malfunction to Mechanism Bertold Schweitzer

Reason, Emotion, and the Context Distinction Jeff Kochan

The Role of Values in Methodological Controversies: The Case of Risk Assessment José Luis Luján et Oliver Todt

Science-based Metaphysics: On Some Recent Anti-metaphysical Claims Matteo Morganti

Theory Success: Some Evaluative Clues María Caamaño-Alegre

Repositioning Realism Emma Ruttkamp-Bloem

Philosophy of Chemistry against Standard Scientific Realism and Anti-Realism Rein Vihalemm

On the Ontology of Linguistic Frameworks Toward a Comprehensive Version of Empiricism Majid Davoody Beni

Quine’s Two Dogmas as a Criticism of Logical Empiricism Artur Koterski

On A.A. Markov’s Attitude towards Brouwer’s Intuitionism Ioannis M. Vandoulakis

The Fitness Landscape Metaphor: Dead but Not Gone Stefan Petkov

Cartesian Forces in a Soulless Physics Zuraya Monroy-Nasr

Exchanging Quantum Particles Tomasz Bigaj

Truth as Contextual Correspondence in Quantum Mechanics Vassilios Karakostas

Decisions without Sharp Probabilities Paul Weirich

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Varia

Constantes logiques et décision Saloua Chatti

Insaisissable Belle au bois dormant Laurent Delabre et Léo Gerville-Réache

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Logic and Philosophy of Science in Nancy (II)

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Preface

Pierre Edouard Bour, Gerhard Heinzmann, Wilfrid Hodges and Peter Schroeder-Heister

1 The 14th International Congress of Logic, Methodology and Philosophy of Science was held in July, 19th – 26th, 2011 in Nancy, the historic capital of Lorraine and birthplace of Henri Poincaré. We were very honored that the President of the French Republic, Monsieur Nicolas Sarkozy, generously agreed his patronage.

2 The LMPS congresses represent the current state of the art and offer new perspectives in its fields. There were 900 registered participants from 56 different countries. They filled 115 sessions consisting of 391 individual talks (among them 6 plenary lectures and 49 invited lectures), 22 symposia (among them 4 special invited symposia), and 13 affiliated meetings and associated events such as 6 public talks—in all nearly 600 papers. These figures reflect the fact that LMPS is not only a place for scientific communication at the highest level, but also a forum for individual and collective research projects to reach a wide international audience.

3 Concerning the program, there were two innovations: 1. For the first time in the LMPS history, the Nancy congress had a special topic: Logic and Science Facing the New Technologies. It illuminated issues of major significance today: their integration in society. These questions were of great importance not only to LMPS participants, but to our professional and sponsoring partners likewise. Correspondingly, a section of the congress was entirely devoted to “Methodological and Philosophical Issues in Technology”. With 16 individual lectures (three invited) and two symposia this special topic made a grand entrance. 2. We put much emphasis on symposia in the “non-invited” part of the program. In addition to four symposia with invited speakers which we organized ourselves, and 13 affiliated symposia related to various topics of the congress, for which their respective organizers were responsible, we issued a call for contributed symposia in addition to the call for contributed papers, giving researchers the chance to apply as a group of up to 6 people for a short symposium on a selected topic. This call resulted in 18 contributed symposia, some of which were of exceptionally high quality.

4 This volume presents a selection of contributed papers. All sections of the congress ranging under the headings General Philosophy of Science are represented in this volume,

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as well as four sections of Methodological and Philosophical Issues of Particular Sciences (Biology, Physics, Chemistry and Economics). A first volume of contributed papers, covering topics in Logic, Philosophy of Mathematics and Cognitive Science, and Philosophy of Technology, appeared in the last issue of Philosophia Scientiæ (18-3), 2014. A selection of invited talks and plenary lectures are published under the title Logic, Methodology and Philosophy of Science. Proceedings of the Fourteenth International Congress (Nancy) by College Publications, London, 2014.

5 We are indebted to many persons and institutions for their integrated efforts to realize this meeting. First and foremost we would like to thank the members of our respective committees, the Local Organizing Committee, and the General Program Committee including its Senior Advisors and Advisors. They all have worked very hard, setting up an outstanding and attractive program and staging it in a comfortable surrounding that would make the congress a scientifically and socially enjoyable event. It has been a great pleasure to work with our colleagues and staff in these committees.

6 We also thank the Executive Committee of the DLMPS for its constant support and encouragement. Claude Debru (Académie des Sciences, Paris) helped us, amongst many other things, with his knowledge of French institutions, for which we are very grateful. Special thanks are also due to the University Nancy 2 and its Presidents, François Le Poultier and Martial Delignon, as well as to the Deans of Nancy’s Faculty of Law, Olivier Cachard and Éric Germain, who willingly let us occupy their splendid lecture halls and facilities. Without the generous financial support of the University of Lorraine, of local, national and international organizations, this meeting would not have been possible. To all these partners we express our warm gratitude.

7 We are also very grateful to many colleagues who helped us in selecting the papers for both CLMPS volumes published as tome 18-31 and 19-1 of Philosophia Scientiæ, and contributed to their improvement through their remarks and suggestions.

8 Last but not least we would like to thank Sandrine Avril, who worked on the LATEX layout of this volume, and took care with her usual competence of a large part of the editorial process.

NOTES

1. A problem occurred in the table of contents of volume 18(3): Prof. Hartley Slater’s contribution, “Quine’s Other Way Out”, does not appear in the paper version. We are very sorry for this omission and wish to apologize to Prof. Slater. This mistake has been corrected in the online version of the journal.

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AUTHORS

PIERRE EDOUARD BOUR Université de Lorraine/CNRS, Nancy (France)

GERHARD HEINZMANN Université de Lorraine/CNRS, Nancy (France)

WILFRID HODGES British Academy (United Kingdom)

PETER SCHROEDER-HEISTER Universität Tübingen (Germany)

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A New Role for Data in the Philosophy of Science

Molly Kao

1 Introduction

1 The problem of theory-ladenness in the philosophy of science has many manifestations. For instance, in the post-logical positivist years, one prevalent strategy for discrediting the strict distinction between observational and theoretical terms was to point out that one’s observational experiences are affected by the theory one brings to bear on the experience (cf. [Hanson 1958], [Kuhn 1970], [Feyerabend 1981]). The problem I will be addressing is not that the phenomenology of specific perceptual experiences can differ depending on the theoretical background an observer possesses. Instead, I will focus on the following problem, which is closer to one raised by Pierre Duhem: the construction of theories requires reliable data, but acquiring reliable data often requires some kind of theory to construct an accurate measuring device. Given this circularity, scientists must be able to provide justification for how they come to certain conclusions based on the experimental data they obtain. I will call this the problem of measurement which is, of course, distinct from the measurement problem of quantum mechanics.

2 In his book Empiricism and Experience, Anil Gupta introduces a novel empiricist epistemology that he believes is able to overcome many of the problems facing classical empiricism [Gupta 2006]. The primary purpose of his book is to argue that we can think of the rational contribution of experience to knowledge as falling within the logical category of a function rather than being propositonal in nature, and that this conception can provide a robust notion of entitlement and justification for our knowledge. In this paper, I explore the possibility of applying Gupta’s account to the structure of scientific theorizing.

3 I will investigate this possibility by studying two examples, one involving thermometry, and one concerning experiments attempting to detect the weak neutral current. I will argue that the data obtained in scientific experiments can be conceived of as playing a functional role in scientific theorizing, analogous to the role Gupta assigns to

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experience in his everyday epistemology. These examples are meant to play a few roles. The first is to address the problem of measurement mentioned above, and to argue that Gupta’s epistemology can provide us with a structure of reasoning that yields good justification for the judgments made in such cases. Secondly, although to defend aspects of Gupta’s account is beyond the scope of this paper, I hope that outlining a plausible way in which to conceive of measurement in scientific practice using Gupta’s epistemology will lend weight to the view he espouses.

4 I will begin by providing an overview of Gupta’s empiricism in section 2. I will outline how his epistemology can be applied to understand the role of data in scientific theorizing in section 3. I will then clarify these claims in section 4 by examining two cases. Section 5 will present some possible objections and responses, and I will conclude in section 6.

2 Gupta’s reformed empiricism

5 Gupta’s empiricism is born of a desire to respect the idea that “experience is the principal epistemic authority and guide” [Gupta 2006, 4] as well as the idea that any particular subjective experience can be produced in multiple ways. His goal is to provide a brand of empiricist epistemology that incorporates these ideas, while not succumbing to some of the pitfalls of classical empiricism. In particular, Gupta is concerned to reject the idea that what is given in experience is propositional in nature.

6 Gupta’s suggestion is to consider experience as falling into the logical category of a function. Thus, we must take seriously the idea that an experience alone cannot justify perceptual judgments: for judgments to be considered rational, they must be made over a background conception of oneself and one’s place in the world. A subject’s conception of herself and her conception of the world are interdependent. One is licensed to certain judgments only when one holds a particular view of the world, but one’s view of the world is constantly being changed by the experiences one is having. It is key that the rationality of making certain claims is relative to one’s conception of one’s relationto the world.

7 For our purposes, we can consider a view to be a combination of judgments, propositions and concepts. An experience provides a mapping from a view to perceptual judgments. Schematically, if e is an experience, and v is a view, the logical

contribution of experience is a function Γe. Γe(v) refers to a class of schematized propositions that the subject is licensed to make, given her view and the experience she has. Gupta presents it thus:

View v ⇒ (Experience e ⇒ Perceptual judgments Γe(v)). 8 Thus, experience merely provides a rational link between views and judgments, and a reasonable view must accompany an experience to produce a reasonable judgment. Moreover, even after undergoing a particular experience, a subject may not be wholly

entitled to the judgments thus produced. To see this, consider Γe(v) a class of propositions, containing the judgment Q. It may be that the subject holds view v and

undergoes experience e, where Q ∈ Γe(v), and to update her view, the subject merely has to add Q to v. However, adding Q to v may make v inconsistent. In this case, she is not entitled to the judgment Q, and she must revise her view accordingly.

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9 However, there seems to be a problem: if the entitlement to judgments that comes from experience is purely conditional, how do we ever acquire categorical entitlement to certain statements? Gupta’s solution draws on the idea of a revision process. He uses experience to generate a revision process on different views and then finds the core of agreement between those views that results.

Consider an ideally rational agent. He will initially hold a view, v0, and will undergo a

succession of experiences ℰ = ⟨e0, e1, …, en, …⟩. At each stage n, the logical role of

experience en is given by Γen, a mapping from the view the subject holds at that point to a new view. Thus, at each stage, a subject revises his view according to the nature of the experience. Sometimes, the revision consists merely of adding a judgment Q; at other times, revision may be a much more involved procedure in which contradictions are

discovered and discarded. Thus, a sequence of experiences ℰ acting on initial view v0

will generate a sequence of views, = ⟨v0, v1, …, vn, …⟩. Gupta calls the revision sequence

generated by ℰ and v0, where n refers to the view at stage n. A sequence of views is stable iff there is a stage n after which all subsequent changes result in a view that is

fundamentally equivalent to n, where this simply means that the views all provide basically the same account of the world. Gupta then introduces the notion of virtual identity between different views. Views v and v′ are virtually identical (v ≈ v′) if they are the same aside from minor differences caused by differences in initial views [Gupta 2006, 93]. Two stable revision sequences and ′ converge iff there is a stage n such that

for all m ≥ n, m is virtually identical to ′m. 10 Consider again an ideally rational being. She would be able to conceive of all the views that would be admissible as starting points. She would also be able to imagine the

effects of a sequence of experiences ℰ on each of those views. Take Π ℰ to be the function taking admissible views to revision sequences and call it a revision process.

Then the revision process Πℰ is strongly convergent iff there is a stage m where all the revision sequences become virtually identical. “Strongly convergent processes generate absolute rational obligations” [Gupta 2006, 98]. If all admissible views were to converge to virtually identical ones, a rational agent would be obligated to hold that view. Furthermore, even if the sequences of views generated by a revision process disagree on details, whatever core of agreement exists would also impose rational obligations on the agent. Thus, convergence is what provides categorical entitlement in Gupta’s account. In the next section, I will reinterpret these ideas in the context of epistemology of science, and in particular, apply it to the problem of measurement.

3 A new role for data

11 In the following, I will refer to “data” in a way that closely follows the definition given by Bogen & Woodward in [Bogen & Woodward 1988].1 However, for my purposes, it is not important to take data as a contrast to phenomena, and I will speak of data simply as providing evidence for changing our theories. I take “data” to refer to the individual results of observations or measurements. Woodward describes data roughly as what registers on a measurement or recording device in a form which is accessible to the human perceptual system, and to public inspection [Woodward 1989, 394]. Data need not be strictly numerical, for they can refer to the results of a number of different

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detection procedures such as temperature readings, scores on psychological tests, and spark detector photographs [Bogen & Woodward 2005].

12 We now return to the problem of measurement and how it may be resolved. My suggestion is to adapt Gupta’s epistemological structure to apply to scientific investigation. The adaptation is a natural one: we simply take a scientist’s background theory to play the role of Gupta’s “view”, and consider the rational role of data as providing entitlement to certain claims, conditional on the scientist’s background theory and the data. Data on their own do not license us to make judgments, just as experience itself does not license judgments. Rather, one must have a background theory, and data play the role of providing a mapping from the original background theory to a revised theory. A series of experiments is analogous to a sequence of experiences, and the course of experimentation induces a succession of theories, each time revised according to the data obtained, just as a sequence of views is revised according to an agent’s experiences. In ideal cases, convergence between different initial views ensues. In such cases, we can explain why data are not cripplingly theory- laden. Although data do not provide justification for claims apart from a theory, this is not to say that there cannot be justification for any claims. Rather, unconditional justification arises when there is convergence between different theories.

13 One aspect of Gupta’s epistemology that makes it appropriate for an epistemology of science is his claim that what constitutes perceptual beliefs can shift, depending on the context. Perceptual judgments refer to those judgments that are immediately yielded by an experience in conjunction with a view, and need no further justification. However, in cases where one’s view is challenged, that immediate entitlement may no longer exist, and so the judgment would not count as perceptual. For instance, the claim “The apple is red”, may count as a perceptual judgment in normal circumstances, but if one is then told that she is in a room with unusual red lighting, the entitlement to that claim is undermined. This is in line with Prajit Basu’s claim that in science, what counts as “raw data” depends on both the context of the experiment and the background knowledge being taken for granted by the scientific community [Basu 2003]. He argues that evidence for a theory is constructed within that theory from (raw) data, but the move from data to evidence can occur at many levels. This can easily be explained in Gupta’s framework. Certain data license one to certain judgments only in conjunction with a background theory, and in the absence of shared views in scientists’ background theories, it will be impossible for the same data to have the same rational import. In the next section, I will present some examples to make explicit the application of this framework.

4 Two examples

4.1 Measuring temperature

14 My first example will demonstrate the problem of testing measurement devices without circularly justifying their use. The history of thermometry is a long one, so I will focus on one stage, when reasonably reliable thermometers had been developed and it was standard to calibrate them according to the freezing and boiling points of water. It seems, though, that in order to determine the thermometer that most accurately gives the temperature between these points requires knowledge of the

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temperature of the substance being measured, i.e., an accurate thermometer. This example demonstrates how convergence between different views can yield categorical entitlement on certain questions. All my historical information will be drawn from the excellent and detailed study presented by Hasok Chang in his Inventing Temperature [Chang 2004].

15 One important debate in thermometry was focused on the best choice of fluid for determining the temperature of a substance, where two main contenders were mercury and air. Jean-André De Luc tried to solve the problem by using the “method of mixtures”, in which different proportions of water at the boiling and freezing points were mixed together. Thus, a mixture of 75% boiling to 25% freezing water was assumed to have a temperature of 75 ° C. As a proponent of the mercury thermometer, De Luc wished to show that it would yield measurement results that were very close to the calculated value, and his experimental results were indeed quite close. De Luc also conducted comparative experiments, where he compared the calculated degree of real heat with thermometers filled with substances other than mercury. The mercury thermometer yielded the most accurate results. De Luc thus concluded that the mercury thermometer gave the best approximation to the real temperature.

16 I claim that it is possible to understand the role of the data in De Luc’s theorizing as entitling him to certain judgments, which he then had to incorporate into his view. Presumably, each measurement result allowed De Luc to infer something specific. For instance, De Luc may have obtained the first measurement result for water calculated to be at 75 ° , and concluded that “The mercury thermometer shows 74.7 ° when the water is at 75 ° .” A reading of 37.0 ° from the thyme oil thermometer for water that was calculated to be 40.0 ° allowed him to conclude “The thyme oil thermometer reads 37.0 ° when the water is at 40.0 ° .” A reading for the alcohol thermometer allowed him to conclude “The alcohol thermometer reads 33.7 ° when the water is at 40.0 ° .” Incorporating these into his view would then allow him to conclude that “The thyme oil thermometer is more accurate than the alcohol thermometer.”

17 In providing the structure of De Luc’s theorizing, it is important to realise what was part of his view: one important feature was that he believed that the method of mixtures was an accurate way of preparing water at a certain temperature. Given this, and given the data that he obtained, he was justified in accepting the judgments that he did. As it turns out, this assumption (and several others) were later challenged; when this occurred, De Luc’s entitlement to the judgments about the readings of the mercury thermometer was undermined, and further work had to be done.

18 I will now consider some of the subsequent developments in thermometry and explain how these fit naturally into the framework being put forth. It will be necessary to start by outlining the admissible views, in this case, opinions about what type of thermometer provided the most accurate measure of temperature. These opinions were often substantiated by specific theories of heat and molecular motion. The first view under consideration was De Luc’s. A different view that issued direct challenges to some of the aspects of De Luc’s view was the newly emerging caloric theory of heat. This theory held that caloric was a subtle fluid that was either the cause of heat, or heat itself. On one variety of this theory, the amount of caloric in a substance is a product of the substance’s capacity for caloric and its temperature. Thus, if a certain body preserved its heat content (the amount of caloric) but its capacity for caloric was raised, its temperature would go down. One of the theory’s most prominent proponents

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was John Dalton, who was able to challenge De Luc’s use of the method of mixtures. Dalton argued that when hot and cold water were mixed, there was a slight decrease in overall volume. According to Dalton’s view, this meant that there was less room for caloric to fit into that water, and so there would be a decrease in heat capacity, or capacity for caloric. Thus, the temperature would go up, with the result that De Luc’s “method of mixtures” calculations would give a temperature that was actually too low. This is analogous to the phenomenon Gupta describes as the shift in what constitutes perceptual judgments, depending on the context. When De Luc was experimenting, he obtained certain thermometer readings, and was licensed straightforwardly to the judgment “The mercury thermometer shows 74.7 ° when the water is at 75 ° .” By challenging De Luc’s view, Dalton also challenged his entitlement to that judgment.

19 A view that emerged later with respect to the question of the most reliable thermometric fluid was that of Henri Victor Regnault. Rather than designing his experiments based on a particular theory of heat, he carried out a series of experiments intended to test the concept of “comparability”. As Chang explains: If a thermometer is to give us the true temperatures, it must at least always give us the same reading under the same circumstance. [Chang 2004, 77]

20 Thus, Regnault’s view regarding the best thermometer did not include a theory of heat or molecular motion; instead, it included a principle about what constituted “best” when judging the accuracy of thermometers. Regnault also did not begin with a view that took either mercury or air thermometers to be superior; his initial view was neutral on the question, and he revised it in light of the data he obtained.

21 Regnault proceeded to carry out a number of experiments to test comparability. One of his tests was designed to compare the values given by mercury thermometers for the same substance: a variety of mercury thermometer readings for the same substance were compared to a reading from an air thermometer. As it turned out, different mercury thermometers made with different types of glass gave different readings. Here, different data allowed Regnault to form judgments such as “The mercury thermometer made with ordinary glass reads 149.80 ° when the air thermometer reads 150 ° ”, and “The mercury thermometer made with crystal reads 150.40 ° when the air thermometer reads 150 ° .”2 When the judgments from the data were incorporated, he was then able to draw a conclusion about the comparability of those thermometers, or the lack thereof. Experiments on different types of air thermometers yielded much more positive results. Such data, along with Regnault’s commitment to the idea that comparability provided the best standard for evaluating thermometers licensed him to certain judgments. Anyone who shared the idea that comparability was an important standard, but held that mercury thermometers were the superior instruments, would have to revise their view in light of such data.

22 I argue that we can see this progression as an instance of convergence of views, providing us with categorical entitlement to the idea that the air thermometer was the most accurate of the choices, given the data that were produced. We began with different views as to what constituted the best thermometric fluid. A series of data caused a change in all of those views. The core of agreement at the end of the series of experiments was that the air thermometer provided a more reliable measure of temperature than other types of thermometers. If a different sequence of data had been obtained, working scientists would have been rationally obligated to a different set of beliefs that constituted the core. For instance, if Regnault’s tests on the mercury

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thermometer had shown that they satisfied the standard of comparability, he would have had to revise his view that was neutral between air and mercury thermometers. This would have been in agreement with De Luc’s views, providing a different example of convergence between two different initial views, revised in the light of experimental data.

23 It is important to note that what did not result from this data was convergence with respect to the underlying theoretical views. The experiments did not license scientists to make judgments that could affect those views. However, even without a definitive theoretical account, the convergence of several views regarding thermometric fluids entitled scientists to a core of agreement. Other experiments and other data would have to be used in order to come to a consensus on different questions regarding heat. This shows that the idea of a “view” in science can be as fine-grained as we wish to take it; scientists may have a view with respect to a particular question, e.g., the best fluid for thermometry, or they may have a view on a more theoretical question, e.g., what constitutes heat. There will certainly be overlap between such issues, but I take it as a virtue that we can conceive of views so flexibly, since scientists are often concerned with particular questions, and it is desirable to have an account of scientific reasoning that can apply in all those contexts. When convergence is achieved on a particular question, then scientists are entitled to that view, although there may have been erroneous elements influencing the data acquisition. Convergence here shows that although certain theories may have been involved in constructing views, and perhaps in constructing measurement devices, agreements can ensue, eliminating the vicious circularity. If we conceive of data as functional rather than a foundation on which to build further theory, its role becomes unproblematic.

4.2 Detecting weak neutral currents

24 In the last section, I discussed an example where the data licensed experimenters to judgments whose contents straightforwardly stated numerical values obtained in the measurements. In this section, I will discuss the use of photographs of bubble chambers in order to detect weak neutral currents.3 I will not treat it in great detail, but it will be useful to see how this account of the role of data can easily accommodate data that is non-numerical in character, and is thus not easily thought of as yielding a judgment that is merely its sentential expression.

25 In 1973, physicists were able to detect weak neutral currents through a series of experiments. At CERN, this was done by firing a neutrino beam into a bubble chamber and taking photographs of the results. According to Bogen & Woodward, The data obtained at CERN consisted of approximately 290,000 bubble chamber photographs of which roughly 100 were thought to provide evidence for the presence of neutral currents. [Bogen & Woodward 1988, 315]

26 In this case then, the data consisted of a set of photographs. In order to understand the role of this data in theorizing from our Guptan perspective, we consider these photographs as licensing certain judgments, given a particular background theory. I will argue that this is precisely the role that the photographs play.

27 One of the factors that made this experiment problematic was the fact that there are other interactions that mimic the behaviour of neutral currents. When a neutrino enters the chamber, either a charged current interaction or a neutral current

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interaction may occur. Both types of interactions produce a shower of tracks, but a charged interaction will also produce a high energy muon, which leaves its own track. However, the neutrino also interacts with the chamber in such a way that it may produce neutrons which interact with other particles in the bubble chamber, imitating a neutral current interaction. This phenomenon thus produces false positives for neutral current interactions. It was necessary to have accounted for this “neutron background” in order to assert that the photographs were genuinely evidence for neutral currents. There were experimenters who used different techniques to establish an upper bound on this neutron background. For those holding the view that this upper bound was correct, the collection of photographs allowed them to judge that some photographs were displaying weak neutral current interactions. Without the belief that such an upper bound existed, scientists would not be licensed to this claim.

28 I submit that here, unlike in the temperature measurement examples, there is no clear way to conceive of either a particular photograph or the collection of photographs as yielding a statement that obviously captures their content. The judgments scientists were licensed to make from individual photographs were something like “This is a picture of blobs and flashes”, which could then be incorporated into their view that would allow them to infer that the pictures represented a possible neutral current interaction. However, such a statement is not the same thing as the image itself, and so it is more reasonable to think of the photographs (the data) as allowing certain judgments to be made. The collection of photographs would then license a judgment such as “There are 100 photos displaying these patterns of blobs and flashes.” This, in combination with the view that held that the upper bound of the neutron background was lower than what was found in experiments licensed inferences about neutral currents. Thus, we can think of the photographs as allowing for an inference, given someone’s view of the apparatus and othertheoretical factors.

5 Some possible objections

29 One obvious objection to this account of scientific theorizing is that it is not realistic to expect different scientific theories always to yield convergence. It may happen that a long string of experiments never causes multiple views to fully converge. Moreover, the opposite scenario can and has occurred. Scientists have believed that they possess categorical entitlement to a view, or at least to a set of beliefs, only to discover at some later date that these views have been incorrect. I grant both points, but I do not think that these are truly objections to the framework that has been set out. In the first case, it is perfectly natural that multiple views will not necessarily converge—the lack of convergence is very often what incites scientists to design more experiments and collect more data. However, even in cases where views do not become virtually identical, they will often contain a core of agreement. In these cases, scientists are categorically entitled to those statements, even though both general views remain rational. As for the second case, this also makes good sense given the history of science. Because we are not ideal beings, scientists cannot possess all possible theories at the beginning of the course of experimentation. The “correct” view may not even be in the realm of possibility given the theoretical resources at hand. Thus, there are cases where scientists’ available views have converged, but new data (combined with their current theories) forces them to make judgments which render their previous views

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inconsistent, and therefore obliges them to revise their views. This process may generate several new views, and the search for convergence continues. This explains why scientists are rational to continue their scientific inquiry in this way.

30 Another problem one might raise is that this account does not necessarily make the revision rule algorithmic, either for the commonsense view, or for scientific enterprises. However, I would argue that the rule of revision need not be perfectly algorithmic, nor must it be unique. We can grant that there are different ways to make rational decisions without denying that the epistemological role of data in scientific investigations are to allow scientists to make judgments. Certainly more work would have to be done in order to outline how we know what judgments we are licensed to make, given a view and data. I suspect that these factors would be highly contextual, and depend on the phenomena under investigation.

31 A different concern might be that even if Gupta’s account of empiricism works for the commonsense view, it does not extend so easily to science since the nature of data differs phenomenologically from the nature of experience. Experience just is a phenomenological occurrence, whereas data goes far beyond a subject’s phenomenology. The relation between experience and allowable perceptual judgments seems much more direct than the relation between data and the judgments one is entitled to due to that data. While it is true that data is quite different from “experience” phenomenologically speaking, this does not negate the possibility of their playing the same logical role. On Gupta’s account, the “direct awareness” aspect of experience is merely a byproduct of our constitution. The character of experience is not the primary contributor to the force of rational experience. Thus, it is not problematic that data do not share this subjective character. What matters is that they play similar roles in their respective realms of reasoning.

6 Conclusion

32 I have argued in this paper that Gupta’s novel empiricism can plausibly be used in the philosophy of science to account for the problem of circularity in measurement. In particular, I hope to have shown that conceiving of data as playing a functional role, and providing hypothetical entitlement to certain judgments, makes sense of the epistemological structure of scientific investigations. By assigning data this role, scientists can gain categorical entitlement to judgments when convergence occurs over possible views, or even over small parts of views. The examples I have given are merely a small start—it would require far more work to show that the same epistemological picture could be applied in more complex situations. Nevertheless, it appears to be a promising account of what justifies scientists in some of their claims, and I believe could be fruitfully extended.

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BIBLIOGRAPHY

BASU, Prajit K. [2003], Theory-ladenness of evidence: A case study from history of chemistry, Studies in History and Philosophy of Science – Part A, 34(2), 351–368, doi:10.1016/ S0039-3681(03)00022-0.

BOGEN, James & WOODWARD, James [1988], Saving the phenomena, The Philosophical Review, XCVII(3), 303–352.

—— [2005], Evading the IRS, in: Idealization XII: Correcting the Model: Idealization and Abstraction in the Sciences, edited by R. Jones, M. & N. Cartwright, The Netherlands: Rodopi, 233–268.

BOGEN, Jim & WOODWARD, Jim [1992], Observations, theories and the evolution of the human spirit, Philosophy of Science, 59(4), 590–611.

CHANG, Hasok [2004], Inventing Temperature: Measurement and Scientific Progress, New York: Oxford University Press.

FEYERABEND, Paul K. [1981], Realism, Rationalism, and Scientific Method: Philosophical Papers, vol. 1, New York: Cambridge University Press.

GUPTA, Anil [2006], Empiricism and Experience, New York: Oxford University Press.

HANSON, Norwood Russell [1958], Patterns of Discovery: An inquiry into the conceptual foundations of science, New York: Cambridge University Press.

KUHN, Thomas S. [1970], The Structure of Scientific Revolutions, Chicago: University of Chicago Press, 2nd edn.

WOODWARD, Jim [1989], Data and phenomena, Synthese, 79(3), 393–472, doi:10.1007/BF00869282.

—— [2000], Data, phenomena, and reliability, Philosophy of Science, 67 (Proceedings), S163–S179.

NOTES

1. This distinction is discussed further in [Woodward 1989, 2000] and [Bogen & Woodward 1992, 2005]. 2. Data is taken from [Chang 2004, 80, Table 2.4]. 3. My discussion here will be simplified, but will follow the example as laid out in [Bogen & Woodward 1988, 2005; Woodward 1989].

ABSTRACTS

There exists a problem of the circularity in measurement: construction of theories requires reliable data, but obtaining reliable data requires reliable measurement devices whose construction requires a theory. I argue that adapting Anil Gupta's empiricist epistemology to a scientific context yields a possible solution. One can consider the role of data not as providing a

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foundation for a theory, but as acting functionally, licensing revisions of a previous theory. Data provide scientists with entitlement to their claims conditional on their background theory. Unconditional entitlement is obtained when different starting theories converge to the same view over the course of experimentation. I explain this idea using two examples, one in thermometry and one involving experiments on the weak neutral current.

Il existe un problème de circularité de la mesure : la construction des théories requière des données fiables, mais obtenir des données fiables requière des dispositifs de mesure dont la construction requière une théorie. Je soutiens qu'une possible solution à ce problème peut être trouvée en adaptant l'épistémologie empiriste de Anil Gupta au contexte de la science. On peut considérer les données, non comme un fondement pour la théorie, mais comme jouant un rôle fonctionnel, celui de rendre licite des révisions de la théorie antérieure. Les données autorisent les scientifiques à accepter des énoncés scientifiques sous la condition des théories d'arrière-plan qui sont les leurs. Une autorisation inconditionnelle est obtenue quand les différentes théories de départ convergent sur la même conception au cours de l'expérimentation. J'explique cette idée en utilisant deux exemples, l'un relevant de la thermométrie, l'autre mettant en jeu les expériences sur les courants neutres faibles.

AUTHOR

MOLLY KAO The University of Western Ontario (Canada)

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From Malfunction to Mechanism

Bertold Schweitzer

1 Introduction

1 This paper advances the idea of exploring the intersection, largely neglected thus far, of two fields of research—on malfunction and on mechanism—and of combining the more practical and usually discipline-specific results of how to gain insights about normal structure and function from the analysis of malfunctions with the more theoretical and systematic understanding of how to examine mechanisms in general.

2 Malfunctions—including deficits, errors, anomalies, breakdowns, or failures1—which are observed in the behaviour of systems may not only contribute to understanding how and why the system is malfunctioning, i.e., diagnosis, or the means by which a normal, functioning state could be restored, i.e., therapy, but also to discover the underlying causes, structures, and mechanisms of the systems affected, both in their functioning and malfunctioning states.

3 Thus, the analysis of malfunctions also contributes to theoretical scientific understanding by discovering and testing hypotheses about a system’s structure, its components and their relations, in short, its mechanism. Such development and testing of theoretical insight concerning normal functioning and its underlying processes and mechanisms based on the analysis of malfunctions can be identified in approaches used in a number of scientific fields, or disciplines. Still, such ideas have not been addressed in general or interdisciplinary methodological studies thus far.

4 On the other hand, a considerable body of literature exists in philosophy of science as well as in natural and social sciences discussing the general methods and strategies for identifying mechanisms responsible for a system’s behaviour [Machamer, Darden, et al. 2000], [Darden 2008], [Hedström & Ylikoski 2010]. The notion of using analysis of malfunctions as an instrument in aid of such strategies is at best mentioned in passing but has not been analyzed systematically yet.

5 Accordingly, the main questions addressed in this paper are: First, in what ways can the analysis of malfunctions, failures, deficits, errors, and related phenomena contribute to

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scientific research, or to understanding the world? Second, in how far are research strategies involving malfunctions, or inferences from malfunction to normal function, methodologically sound and yield reliable scientific conclusions? Third, how can the analysis of malfunctions help in identifying causal connections and unraveling complex causal mechanisms?

6 These questions arise because malfunctions are de facto being analyzed, either systematically, or on an ad hoc basis, in many different disciplines, from biology and psychology to linguistics and sociology. If coupled with methodological reflections at all, malfunctions have often been praised for offering valuable and sometimes unique insight into the subject of investigation. Fromkin points out that Speech error data do […] provide us with a “window” into linguistic mental processes and provide, to some extent, the laboratory data needed in linguistics. [Fromkin 1973, 43]

7 However, concerns have been voiced as well, pointing out that inferences from malfunction to normal function are by no means straightforward: Gregory comes to the conclusion that “[...] arguments from malfunction to normal function are fraught with difficulties even for quite simple machines” [Gregory 1981, 85]. Moreover, general doubts as to the usefulness of the analysis of malfunctions have been expressed. It has even been claimed that inferences based on malfunctions might be outright misleading.

8 Since a general, systematic analysis of malfunction-based research strategies has not been undertaken yet, this paper shall try to provide some arguments to evaluate these competing claims concerning the role and value of malfunctions in order to close this gap in philosophy of science.

9 This paper will try to show, first, that the identification and analysis of malfunctions provide an opportunity for insights into the normal operation of the entities in which they occur; second, that the most typical features, aims, and results of malfunction- based research strategies lie in the decomposition of systems, the identification of sequences and chains of events, the localization of subsystems; culminating in the elucidation of complex mechanisms; third, that malfunction-based research strategies follow a certain common pattern, or logic; fourth, that this logic connects well with independently developed and commonly used strategies for the discovery of mechanisms and testing of mechanistic hypotheses; and, finally, that malfunction- based research strategies are indeed unique and valuable, in that they are neither self- reliantly guaranteeing correct analyses nor wholly misleading; instead they can and should be used, in particular in a heuristic role, but should be backed up, wherever possible, by complementing methods in order to obtain reliable conclusions.

10 The account offered here is based on description, comparative analysis and rational reconstruction of empirical research actually carried out in various scientific disciplines. The general patterns emerging from this comparison are in turn related to independently developed accounts of general strategies for analyzing mechanisms. Moreover, the general validity of inferences from malfunction to function is evaluated in order to determine to what extent these kinds of inference can indeed be rationally justified.

11 This paper’s overall argument will be structured as follows: section 2 presents examples of malfunctions pointing out how their analysis contributes to theoretical understanding and scientific knowledge. Section 3 provides a more specific explication of the concept of malfunction. Section 4 explains typical features, aims, and results of

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malfunction-based research strategies. Section 5 discusses strategies for discovery and analysis of mechanisms and relates them with malfunction-based approaches. Section 6 offers general theoretical conclusions and implications.

2 Malfunctions in use

12 Some instructive examples of how observation and analysis of malfunctions can advance research come from the field of behavioural studies: If [...] the observer of captive animals sees the way in which a young wolf or dog carries a bone to behind the dining room drapes, lays it down there, scrapes violently for a while next to the bone, pushes the bone with his nose to the place where all the scraping was done and then, again with his nose and now squeaking along the surface of the parquetry flooring, shoves the nonexistent earth back into the hole that has not been dug and goes away satisfied, the observer knows quite a lot about the phylogenetic program of the behavior pattern. [Lorenz 1981, 48]

13 Thus, the researcher gains theoretical insight from the observation of a characteristic pattern of malfunction. This shows convincingly, in particular if the young wolf or dog has never had the opportunity of digging holes in the ground before, not only that innate components of behaviour exist, but also which particular patterns they assume without, or before being influenced by the environment.

14 Another discipline where malfunctions contribute to theoretical knowledge is genetics. Here, too, the observation of malfunctions and tracing these back to underlying processes, in particular, genetic mutations, plays an important role. One striking example is the antennapedia mutant of the fruit fly Drosophila. Here, normal individuals (the so-called “wild type”) have antennae on their forehead which, in the antennapedia mutant, are replaced by legs. This observation and the subsequent genetic analysis ultimately led to the discovery of the homeobox, a DNA sequence regulating patterns of anatomical development in animals, fungi and plants [McGinnis, Levine et al. 1984].

15 A third field where malfunctions have contributed strongly to theoretical insight is the psychology of perception. Here, optical illusions have played a major role in both demonstrating the imperfections of perception while at the same time assisting in tracing them back to the details of perceptive mechanisms. The Hermann grid illusion, e.g., misleads the eye into perceiving grey blobs at the intersections of a white grid on a black background, with the blobs disappearing when focused directly. This illusion can be explained by a process of lateral inhibition involving nerve cells in the retina: ganglion cells receive information from several photoreceptive cells, with stimuli from the centre of its “receptive field” exciting a ganglion cell and stimuli from its periphery inhibiting it. At an intersection of white lines, a ganglion cell receives stronger stimuli from the periphery than its neighbouring cells, leading to a comparatively weaker excitation of the ganglion cell, and resulting in the perception of this spot as less bright that the surrounding white areas [Frisby & Stone 2010] . Thus, insights from the demonstrable malfunctioning of our visual sense lead to hypotheses about the structures and processes underlying normal vision.

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3 Characterizing malfunction

16 After having introduced the phenomenon “malfunction” by a few examples, can we be more specific about how it should be characterized in the present context? Five considerations seem important:

17 First, the term malfunction, both in its everyday sense and when discussed as a tool for scientific research, is usually understood as describing any case of something going wrong. This, of course, requires the possibility of comparing such a case with a background of cases where something similar is “working well” or “working as expected”. Thus, the term “malfunction” can sensibly only be used in cases where a corresponding function is either known, or at least assumed hypothetically. Moreover, analyses of malfunctions typically require the comparison of one or several different variants of malfunction with a normal function. Therefore, the comparison of malfunction with function involves the comparison, within the same general type, of one or more “functioning” tokens with one or more “malfunctioning” tokens.

18 Second, malfunction may be defined in a roundabout fashion as any kind of absence of or deficiency in some function. This definition seems straightforward, but of course in turn requires an appropriate definition of “function”. This, however, is complicated by the fact that two different, contested definitions of “function” have been proposed. One such definition is based on an etiological view, looking to the history of an item to define its function as its contribution to the survival and reproduction, or in other words, the fitness of an organism it is part of [Millikan 1984]. Artifacts, in this view, may derive functions in case they contribute to the fitness of organisms. The competing definition is based on a causal role view, defining function as the causal contribution of some entity towards the capacity or operation of a larger system containing this entity [Cummins 1975].

19 The etiological definition of function seems narrower and more precise. However, it denies the status of function to many phenomena for which the term is commonly used. In particular, we would never be able to decide whether we can legitimately consider something to be a function unless the history of the item in question had been considered. Basing a definition of malfunction on an etiological definition would also prevent us from using “malfunction” in many cases where researchers themselves use this term, or closely related ones.

20 In what follows, therefore, the definition of “malfunction” will be based on the causal role view since this promises to provide a suitably inclusive concept of function. Accordingly, “malfunction” will be defined as any case in which a “function”, understood as a causal contribution of some entity towards the capacity or operation of a larger system containing this entity, and understood as being present in “normal” cases, or tokens of a type, is absent, weakened, or modified in a way that the original function is no longer present.

21 Third, it should be emphasized that labelling a phenomenon as a “malfunction”, in particular when humans are concerned, should never be understood in an evaluative or pejorative sense.

22 Fourth, these considerations clarify that the scope of any malfunction-based strategy is limited to fields where functions and malfunctions—at least in the wider causal role sense—can be associated with the target items. Thus, we may expect malfunction-based

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strategies to play a role in biology, psychology, linguistics, and social sciences as well as in sciences of artefacts, such as technology, but not, e.g., in physics.

23 Fifth, malfunction-based research strategies need to be sharply distinguished from all kinds of strategies based on “learning from error”, or “trial and error”, or falsification, where the main goal is identifying and rejecting erroneous hypotheses. In malfunction- based research strategies, the main focus is on the malfunctions of target items, not on the (potential) failure of hypotheses about these items. Of course, researchers search for potential errors in their hypotheses and theories, and sometimes analyses of such errors do indeed contribute to finding “truer” theories [Wimsatt 1987]. This, however is still different from employing malfunction-based research strategies to theories. This would amount to analyzing malfunctions of theories in order to achieve deeper understanding of how theories work in general, i.e., theory structure and theory dynamics. This question, though it appears to be a promising one, is not the subject of this article.

4 Inference from malfunction

24 Now, let us consider somewhat more in-depth which discoveries, or inferences can typically be achieved by using malfunction-based research strategies. Six of these stand out: first, discovery of the existence of hidden systems and subsystems ; second, decomposition of a system into modules; third, identification of sequences and chains of events in processes; fourth, physical localization of modules inside a system; and fifth, contributions to the testing of mechanistic hypotheses.

25 First, spontaneously occurring malfunctions can draw attention to the existence of systems, or substructures of systems that have hitherto escaped researchers’ notice. The existence of constancy mechanisms, e.g., might not be obvious: being used to a constant room temperature, only the failure of a thermostat might draw attention to the fact that a complex control system is required to maintain a constant temperature. Moreover, the existence of substructures with an item performing a complex function might only become apparent when specific parts of the overall function are lost while others continue to work as usual. One example are the various specific impairments that can result from brain injuries, such as prosopagnosia, or face blindness, where the ability to recognize faces is severely reduced, while the ability to recognize other objects remains relatively intact. In this way, malfunctions may provide a unique insight into structures that are normally hidden, or transparent, and cannot be observed in or inferred from normal functioning systems alone.

26 Second, decomposition, or fractionation of a system into discernible functional or structural subsystems, or modules is often among the initial contributions an analysis of malfunctions can provide. This step moves beyond the mere recognition of the existence of a substructure to identifying and enumerating parts of substructures, usually by comparing different types of malfunctions.

27 One example from biology is the determination of the number of genes involved in a biological process: assuming that two different recessive mutations have been identified that both result in the same observable malfunction (e.g., some aberrant behaviour), then crossing experiments combining the two mutations in one organism may show these two mutants to either complement each other, resulting in normal, or “wild-type” behaviour, in which case the mutants may be inferred to be alleles of two

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different genes, or the two mutants might not complement each other, leading to aberrant behaviour, in which case they are inferred to be defective in the same gene. The first case, therefore, leads to the conclusion that at least two different genes are involved in the process, whereas only one gene can be discerned in the second case.

28 Another example is the identification of cognitive and neuronal modules in the human brain. Brain injuries, strokes, or other processes may lead to the loss of specific capabilities. One example is prosopagnosia, or face blindness, mentioned above. Such “dissociations” are used in (cognitive) neuropsychology to identify the number and the characteristics of functional modules.

29 Critics of this approach, however, have voiced concerns about the reliability of this method. Inferences from associations (with the loss of two functions commonly occurring together) or single dissociations (where one specific function is lost while others continue to function normally) are indeed unreliable. For instance, an associated loss of two capabilities might not happen due to functional commonalities but because of functionally irrelevant anatomical reasons, such as dependence on a common blood supply. So-called “double dissociations”, however, where one capability, A, can be lost while B continues to function normally, but where also B can disappear while A is still intact, are seen by a majority of cognitive neuropsychologists as allowing reliable inference to the existence of two different modules [Jones 1983] [Dunn & Kirsner 2003].

30 An even more fundamental concern is that malfunction-based strategies might also break down in case the target system’s structure turns out to be quite unlike a hierarchical mechanism, as for instance in a connectionist system [Bechtel & Richardson 1993]. To what extent, however, purely connectionist systems could exhibit, when damaged, for instance classical forms of double dissociations is not clear and should be investigated.

31 Third, malfunctions contribute to the determination of the order of steps in sequential processes. One example from biology is the identification of the sequence of steps involved in biochemical processes, e.g., the biosynthesis of the amino acid arginine. Here, a number of different mutants with defects in different genes are used, none of which can grow without arginine. Since mutations are blocking different enzymatic reactions in the metabolic pathway for the synthesis of arginine, different intermediate metabolic products synthesized before each defective step can accumulate in cells. Mutants with defects earlier in the process can be cross-fed by mutants with defects later in the pathway, since later mutants can provide earlier ones with substances needed for growth [Stanier, Ingraham et al. 1987]. Thus, analyzing the patterns of possible cross-feeding indicates the sequence of genes and biochemical steps involved.

32 A fourth type of inference allowed by an analysis of malfunctions is localization: by correlating data on malfunctions with information on sites of physical damage, physical localization of the corresponding function may be achieved. An example from neuropsychology illustrates this: based largely on lesion studies in monkeys, two main routes for processing visual information have been distinguished. One route analyzes “the physical properties of a visual object (such as its size, color, texture and shape)” and constitutes the so-called “what” system, whereas an anatomically different route is involved in “perception of spatial relations among objects, and not in their intrinsic qualities”, called the “where” system [Mishkin, Ungerleider et al. 1983].

33 This type of localization in particular has been criticized for being too simplistic:

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The effects of removing or modifying, say, the line scan time-base of a television receiver would be incomprehensible if we did not know the engineering principles involved. Further, it seems unlikely that we should discover the necessary principles from scratch simply by pulling bits out of television sets, or stimulating bits with various voltages and wave forms. [Gregory 1961, 320-322]

34 To others, this seems exaggerated: From time to time it has been argued that one can learn nothing of interest about an intact system when it is broken. The argument often runs like this: given a radio, if you cut off the plug no sound will come out; you would consequently conclude that the plug was the source of the sound. Certainly the village idiot might draw such an inference [...], however, actual scientific research can avoid such naivety: No more than any other field of research is the domain of human deficit studies a haven for village idiots. [Kean-1984]

35 Finally, malfunctions can also offer additional and, in some cases, more severe ways of testing hypotheses compared with tests based on normal functioning alone. For example, a plausible demand is that models should not only show the same performance, but also commit the same malfunctions as the target system, since this would be an indication that the model does not only superficially simulate the target system’s performance but brings about by the same means. In a similar vein, the “goal of speech-error research is [...] to identify, for particular issues of [...] theory, the particular errors or error classes which can provide relevant evidence” and “to find the perfect speech error” [Cutler 1988, 219].

5 Integrating mechanistic and malfunction-based strategies

36 Next, after pointing out characteristic contributions of, or inferences from malfunctions, it appears useful to relate these contributions in a systematic fashion to more general research strategies, in other words, to integrate malfunction-based strategies into more general research strategies.

37 Mechanistic research strategies, here, appear to be the ones malfunction-based strategies could be most easily related to and integrated into.

38 Thinking in terms of mechanisms is considered to be fruitful, and establishing mechanistic hypotheses as well as providing mechanistic explanations is seen as an important goal: “At least in biology, most scientists see their work as explaining types of phenomena by discovering mechanisms” [Wimsatt 1974]. The same holds for many other disciplines, such as psychology, social sciences, and technology, see [Bunge 1997], [Mayntz 2004]. The following definition captures what seems close to a consensus: A mechanism is a structure performing a function in virtue of its component parts, component operations, and their organization. The orchestrated functioning of the mechanism, manifested in patterns of change over time in properties of its parts and operations, is responsible for one or more phenomena. [Bechtel & Abrahamsen 2005, 423]

39 Thus, mechanistic research is concerned with functions, and while malfunctions are rarely being explicitly considered in this body of literature, the relation with malfunctions seems straightforward, if only because “function” is involved. However, the connections, as we will see, reach much further than that.

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40 Strategies for the discovery of mechanisms have been discussed in much detail, see [Bechtel & Richardson 1993], [Machamer, Darden, et al. 2000], [Darden 2008], often distinguishing construction, evaluation and revision of mechanist hypotheses [Darden 2006]. Here, we will focus first on strategies for the “construction” of causal mechanistic hypotheses, in particular “activation” and “modification” strategies [Craver 2002], many motifs of which correspond closely with methods used in the analysis of malfunctions.

41 Activation strategies for the discovery of mechanisms are based on modifying the environment of an item, hoping to evoke a reaction or a change in behaviour. Being able to provoke malfunctions in behaviour is one of the most significant outcomes of activation experiments since this shows that conditions necessary for normal functioning have been affected. Conversely, the observation of a malfunction often triggers a search for changes in the environment possibly responsible for this malfunction. Thus, malfunctions are often significant outcomes of either planned or natural activation experiments.

42 In modification strategies used in discovery of mechanisms, the internal setup of items is modified by the experimenter. They can be divided into interference strategies, also called subtractive strategies, and additive strategies.

43 In mechanistic interference or subtractive strategies some component of an item is diminished, retarded, eliminated, disabled, or destroyed, and the effect or effects downstream or on the system-level are registered [Craver 2002]. Examples of such active manipulations include deletion (“knockout”) of genes, ablation of organs, inactivation of brain regions by chemicals or by cooling, and many others. Quite frequently, observed malfunctions can be traced back to spontaneous or accidental modifications equivalent to such subtractive manipulations.

44 In mechanistic additive strategies, components are stimulated, augmented, intensified, or multiplied, and the effect or effects downstream or on the system-level registered [Craver 2002]. Examples are manifold: providing an excess supply of active biochemical substances, multiplying the number of copies of genes, or stimulating neurons. Again, perceived malfunctions can often be related to spontaneous or accidental modifications equivalent to such additive manipulations.

45 Thus, malfunctions quite often arise as a consequence of spontaneous or accidental analogues of subtractive or additive experimental interventions. Such situations amount to natural experiments in which subtraction or addition occur without interference by an experimenter.

46 With regard to spontaneous malfunctions as well as phenomena resulting from planned experiments, the exact modification or intervention causing the phenomenon may or may not be known, or obvious; in the latter case it needs to be identified or provisionally conjectured. Identifying the cause of an observed malfunction is of course not trivial. One reason is that malfunctions can occur on all hierarchy levels, and the underlying intervention, or spontaneously occurring modification may happen on the same, or a different hierarchy level.

47 As with all natural experiments, one major disadvantage of relying of either spontaneously occurring or randomly provoked malfunction is that the means of controlling both occurrence and the circumstances are missing or very limited. A unique advantage, however, is that malfunctions occur without the need for a

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researcher having good ideas of how and where to intervene by subtractive or additive manipulations. A second advantage malfunctions provide is that their spontaneous occurrence might allow an analysis even where direct manipulation is impossible (e.g., in classical genetics before molecular methods existed) or morally forbidden (e.g., harmful experiments on humans).

6 Conclusion

48 In conclusion, the role of malfunctions in strategies for analyzing mechanisms may be summarized as follows: malfunctions are phenomena that are often surprising, raise attention, and provide information about subsystems, or modules hidden inside other systems. Since many malfunctions are conspicuous or run contrary to researchers’ expectations, they often provide both excellent starting points for and easily detectable markers in investigations. At the same time, many malfunctions are exactly the same kind of phenomena that are sought after, and that experimenters try to produce in common general setups for probing mechanisms, such as subtractive and additive strategies.

49 Typically, malfunction-based research strategies are involved in the generation of mechanistic hypothesis as well as in testing. They contribute by attracting attention to unknown systems or aspects of systems, or by revealing the hidden existence of a system by one of its malfunctions. They may also supply specific information on key features of a system, or provide access to data difficult or impossible to obtain by other means. Finally, they may enable reliable inference to a comprehensive model of the target system; in particular if complete profiles of all possible functions and malfunctions are available. For most of these features of malfunction-based analysis, the roles they play in mechanistic strategies could be identified. This helped to shed light on the exact kind of contribution malfunctions can provide for the discovery and testing of causal mechanistic strategies and how their analysis can complement the methods—mainly experimental—usually considered in mechanistic strategies so far.

50 Using malfunction-based research strategies alone usually cannot guarantee reliable results, not unlike many other strategies used in isolation. At least two important issues may arise when relying on data from malfunctions only: first, patterns of malfunctions may suggest the identification of subsystems, or modules, or the fractionation of a system. Erroneous fractionation, however, might result from secondary commonalities or differences between modules, irrelevant for the primary questions about structure and function. Second, malfunction-based strategies might break down when a system’s structure is radically unlike a modular mechanistic system. Thus, malfunction-based research strategies benefit from the integration of additional evidence—a recommendation in which they are not alone and which is apt for other, e.g., mechanistic strategies, too.

51 These recommendations include searching for separate and independent evidence concerning existence and features of hypothetically assumed entities, activities, or modules, trying to provide support for experimental data by paying attention to control, repeatability, and randomization, gaining additional support by using either techniques or results from multiple fields, and finally attempting integration of individual mechanisms into the larger matrix of scientific knowledge.

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52 All arguments considered, malfunctions and malfunction-based strategies are indeed capable of contributing greatly to scientific research, in particular to the elucidation of mechanisms. The major contribution of malfunction-based strategies, due to their important role in discovery and their strengths in suggesting hypotheses, may be seen in the area of heuristics. However, unfolding their strengths in combination with other adequate strategies, in particular mechanistic ones, malfunction-based strategies do also contribute towards conclusively evaluating hypotheses, and successively refining them. Thus, malfunctions and their analysis should be seen as a very valuable, and sometimes even indispensable component of scientists’ methodological toolkit.

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HEDSTRÖM, Peter & YLIKOSKI, Petri [2010], Causal mechanisms in the social sciences, Annual Review of Sociology, 36(1), 49–67, http://dx.doi.org/10.1146/annurev.soc.012809.102632.

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JONES, Gregory V. [1983], On double dissociation of function, Neuropsychologia, 21, 397–400.

KEAN, Marie-Louise [1984], Linguistic analysis of aphasic syndromes, in: Biological Perspectives on Language, edited by D. Caplan, A. R. Lecours, & A. Smith, Cambridge, MA; London: MIT Press, 130– 140.

LORENZ, Konrad [1981], The Foundations of Ethology, New York: Springer.

MACHAMER, Peter, DARDEN, Lindley, & CRAVER, Carl F. [2000], Thinking about mechanisms, Philosophy of Science, 67(1), 1–25.

MAYNTZ, Renate [2004], Mechanisms in the analysis of social macro-phenomena, Philosophy of the Social Sciences, 34, 237–259.

MCGINNIS, W., LEVINE, M. S., HAFEN, E., KUROIWA, A., & GEHRING, W. J. [1984], A conserved DNA sequence in homoeotic genes of the Drosophila Antennapedia and bithorax complexes, Nature, 308(5958), 428–433, http://dx.doi.org/10.1038/308428a0.

MILLIKAN, Ruth Garrett [1984], Language, Thought, and Other Biological Categories, Cambridge, MA: Bradford Books.

MISHKIN, Mortimer, UNGERLEIDER, Leslie G., & MACKO, Kathleen A. [1983], Object vision and spatial vision: Two cortical pathways, Trends in Neurosciences, 6, 414–417.

STANIER, Roger Y., INGRAHAM, John L., WHEELIS, Mark L., & PAINTER, Page R. [1987], General Microbiology, London: Macmillan, 5th edn.

WIMSATT, William C. [1974], Complexity and organization, in: PSA 1972: Proceedings of the Philosophy of Science Association, edited by K. F. Schaffner & R. S. Cohen, Dordrecht: Reidel, 67–86.

—— [1987], False models as means to truer theories, in: Neutral Models in Biology, edited by Matthew H. Nitecki & Antoni Hoffman, New York; Oxford: Oxford University Press, 21–55.

NOTES

1. Throughout this article, the term “malfunction” will be used as a umbrella term for all of these related concepts. A definition for “malfunction” will be provided in section 3.

ABSTRACTS

Malfunctions, deficits, and errors provide considerable insight into key features of the entities in which they occur. In particular, the careful analysis of patterns of functioning and malfunctioning facilitate discovery, explanation and theorizing about structure, function, and underlying mechanisms of a system. In some cases, malfunctions even supply the unique probe into the internal workings of a system. This essay analyzes methods used by various disciplines involving malfunctions such as mutations, visual illusions, action slips, or speech errors, and identifies common patterns of malfunction-based research strategies that contribute to the decomposition of systems, the tracing of sequences of events, the localization of subsystems, and the generation and testing of complex mechanistic hypotheses.

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Le dysfonctionnement, la défectuosité et les erreurs sont des phénomènes qui peuvent aider à mieux comprendre les entités affectées par ces incidents. L’analyse approfondie du fonctionnement et du dysfonctionnement facilite en particulier la découverte, l’explication et la modélisation théorique des structures, fonctions et mécanismes propres à un système. Dans certains cas, les dysfonctionnements sont le seul moyen d’accéder aux processus internes d’un certain système. Le présent essai analyse les méthodes de diverses disciplines tenant compte de dysfonctionnements tels que les mutations, les illusions optiques, les erreurs d’action ou les lapsus linguistiques et identifie les motifs communs aux stratégies de recherche basées sur le dysfonctionnement. Ces stratégies contribuent à la décomposition de systèmes, à la reconstruction de séquences d’événements, à la localisation de sous-systèmes, ainsi qu’au développement et au test d’hypothèses mécanistes.

AUTHOR

BERTOLD SCHWEITZER University of Dundee (United Kingdom)

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Reason, Emotion, and the Context Distinction

Jeff Kochan

1 Introduction

1 The number of contemporary philosophers who have addressed the question of whether emotion plays a constructive role in scientific reasoning can be counted on one hand, or perhaps two if one tries hard. The most prominent among them are James McAllister, Lisa Osbeck and Nancy Nersessian [Osbeck & Nersessian 2011, 2013], and Paul Thagard. This lack of interest in the epistemic importance of emotions is somewhat puzzling. In recent years, a growing body of influential work by philosophers and cognitive scientists has challenged the prevailing assumption that reason and emotion necessarily conflict with one another. Indeed, emotion has now emerged as a central theme in contemporary philosophy of mind and as a vibrant topic of empirical research in the cognitive sciences. And yet, philosophers of science have given hardly any attention to these developments. I cannot be alone in my surprise that this should be so. In 2002, McAllister could reasonably write: I forecast that the role of emotions in scientific practice will become a leading theme in philosophy of science over the coming decade. [McAllister 2002, 9]

2 Over one decade later, we can see that McAllister’s forecast was too optimistic. Philosophers of science have proven themselves impressively resistant to the exciting developments in emotions research taking place just outside the carefully controlled boundaries of their own philosophical sub-discipline.

3 The question motivating the present paper is: why? This question is sharpened by the fact that there are important precedents in the philosophy of science for interest in the epistemic role of emotion in scientific reasoning, precedents which seem to have now been largely forgotten. There is, for example, the chemist-philosopher Michael Polanyi’s account of “scientific passions”, which ran as a central thread through his better-known discussion of tacit knowledge in scientific practice [Polanyi 1958]. As is well known, Thomas Kuhn was strongly influenced by Polanyi’s views on tacit

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knowledge, but when Kuhn appropriated Polanyi’s work he silently placed the topic of scientific emotions to one side, see [Kuhn 62, 44, n. 1]. In the 1980s, the relation between emotion and scientific reasoning broke once again onto the scene, in the works of feminist epistemologists and philosophers of science. The best-known example is Evelyn Fox Keller’s description of the plant geneticist Barbara McClintock’s “feeling for the organism” [Keller 1983]. (I give detailed attention to Polanyi’s and Keller’s contributions in [Kochan 2013].) In addition, Helen Longino has argued that “our cognitive efforts have an ineluctably affective dimension” [Longino 1993, 108]. The feminist epistemologist, Alison Jagger [Jagger 19 89, 137], furthermore argued that “emotional attitudes are involved on a deep level [...] in the intersubjectively verified and so supposedly dispassionate observations of science” [Jagger 1989, 138]. Yet, even in feminist philosophy of science these insights were not developed in an explicit and deliberate way. Once again, the question emerges: why not?

4 In this paper, I will take a few tentative first steps towards answering the question of why the philosophy of science has been so unresponsive to recent developments in the philosophy of mind and the cognitive sciences. My conjecture is that one important obstacle to philosophers of science recognising the relevance of contemporary emotions research for their own field is their continuing commitment to the original distinction between the contexts of discovery and justification. With the introduction of this distinction in the 1920s, emotion was placed squarely in the context of discovery, whilst the context of justification was declared the principal domain of professional interest for philosophers of science. Although deliberate attention to the context distinction has waned in more recent years, the assumption that emotion makes no contribution to the epistemic justification of scientific beliefs has persisted. I will argue that the force of this assumption relies upon a conception of knowledge that is less compelling than it once was. Recent developments in naturalised epistemology, especially reliabilism, provide a promising way by which to accommodate a constructive role for emotion in scientific reasoning.

2 Reason, emotion, and the context distinction

5 The origins of the context distinction are typically attributed to the early European phase of logical empiricism. According to Alan Richardson, the motivation behind the introduction of the context distinction was a desire to balance the freedom necessary for scientific research with the epistemic responsibility of the scientific community [Richardson 2006, 50]. The early logical empiricists laid out their basic position in their 1929 manifesto, Wissenschaftliche Weltauffasung: Der Wiener Kreis (The Scientific Conception of the World: The Vienna Circle). There, they declared their overriding goal as “unified science” [Vienna Circle 1929, 89]. In this spirit, they emphasized the need for collective effort and intersubjective agreement, which they set out to achieve through the development of a “neutral system of formulae” and a “total system of concepts” in which “dark distances and unfathomable depths” were to be rejected. They sought, in particular, to purge scientific discourse of metaphysical statements. These statements, they claimed, were devoid of meaning; they “say nothing but merely express a certain mood and spirit [Lebensgefühl]”. When re-interpreted as empirical statements, “they lose the content of feeling [Gefühlsgehalt] which is usually essential to the metaphysician” [Vienna Circle 1929, 90]. Such statements belong, not to science, but to

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lyric poetry or music. The idea seems to be that the feelings or emotions expressed in metaphysical statements are hopelessly subjective and resistant to falsification, and so unfit for inclusion in the intersubjectively verifiable system of formulae and concepts which were to constitute the epistemic core of an international and unified scientific culture.

6 Under this remarkably prescriptive vision of the scientific enterprise, scientific statements would be justified only if they were open to formal analysis and intersubjective verification. Writing one year before the appearance of the Vienna Circle’s manifesto, Rudolf Carnap, a co-author of that samemanifesto, argued: It must be possible to give a rational foundation for each scientific thesis, but this does not mean that such a thesis must always be discovered rationally, that is, through an exercise of the understanding alone. After all, the basic orientation and the direction of interests are not the result of deliberation, but are determined by emotions, drives, dispositions, and general living conditions. This does not only hold for philosophy, but also the most rational of sciences, namely, physics and mathematics. The decisive factor is, however, [...] the justification of a thesis. [Carnap 1928, xvii]

7 Here Carnap draws a clear line between the contexts of discovery and justification, placing emotions decisively on the side of discovery. On the side of justification, scientific knowledge was to be understood strictly as a formal system of concepts and formulae, rigorously bound to empirical data by ineluctable chains of logic.

8 When, in 1962, Thomas Kuhn set out to criticise the logical empiricists’ view of scientific knowledge as a formal system of concepts, he did little to question the by- then orthodox opinion that emotion plays no epistemic role in scientific reasoning. Against the analytical formalism of the logical empiricists, Kuhn argued that scientific reason was structured, in significant part, by non-formalisable tacit elements. For Kuhn, the intersubjective agreement which ensured the rationality of the scientific enterprise was conditioned not only by the public transparency of formally explicable rules and concepts, but also by the shared skills and values which resulted from common training within similar intellectual and disciplinary contexts. Although Kuhn rejected the logical empiricists’ formalism, he thoroughly endorsed their emphasis on the intersubjective nature of scientific reasoning.

9 Two specific points deserve special emphasis in concluding this brief historical sketch. First, emotions were tied to metaphysics. They could thus not be fit into an empirically grounded conception of scientific knowledge. Second, emotions were considered to be an individualistic, or subjective, phenomenon. As a consequence, no place could be found for them in the intersubjective, or objective, context of scientific justification. I now wish to argue that a naturalistic account of scientific reasoning may provide a means by which to meet these two objections.

3 The reliability of scientific emotions

10 Among empirical studies of the relation between emotion and reason, the work of neurologist Antonio Damasio is most well known. Based on a series of clinical studies of brain-damaged individuals, Damasio concluded that the capacity to reason is tied to a collection of systems in the brain which are alsoresponsible for the processing of emotions [Damasio 1994, 78]. Damage to the brain’s emotion system is accompanied by

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a dramatically diminished capacity for rational planning and decision-making. More specifically, a loss in emotional responsiveness affects our ability to judge salience between different options, thereby rendering our decision-making landscape “hopelessly flat” [Damasio 1994, 51].

11 Work by the philosopher of emotion, Ronald de Sousa, provides a conceptual framework within which we might better understand the surprising correlation uncovered by Damasio’s clinical studies. Like Damasio, de Sousa argues that emotions “guid[e] the process of reasoning”, that they “underlie rational processes” [de Sousa 1987, 197, 201]. His considerations focus on what he calls the “philosophers’ frame problem” [de Sousa 1987, 193]. The frame problem arises from the recognition that we bring a tremendous store of knowledge to any situation which we face. We constantly draw from this store even in order to interpret the simplest of instructions or to disambiguate the simplest of sentences. To pick a pithy example from de Sousa: think [...] of the general knowledge required to know that snow-shoes, alligator- shoes, and horse-shoes are not respectively made of snow, worn by alligators, or used to walk on horses. [de Sousa 1987, 192]

12 Faced with this superabundance of knowledge, we need to be able to distinguish between what is and what is not relevant to the task at hand. In other words, we need to be able to frame the information available to us in a way which picks out the bits we actually need to pay attention to in order to move forward under those particular circumstances. It is on this basis that de Sousa argues that emotions underlie rational processes, that they are indispensable for our capacity to reason. The function of emotions, he writes, is to deal with the philosophers’ frame problem: to take up the slack in the rational determination of judgement and desire, by adjusting salience among objects of attention, lines of inquiry, and preferred inferential patterns. [de Sousa 1987, 203]

13 By controlling salience, emotions protect us from the sort of deliberative paralysis suffered by Damasio’s brain-damaged clinical subjects, a paralysis which severely impaired their ability to function rationally within the world.

14 For de Sousa, the link between emotion and reason is to be explained ultimately in biological terms. Hence, both he and Damasio recommend a thoroughly naturalistic explanation for the epistemic role played by emotion in the reasoning process. An important feature of such a methodology is that it conceptualises knowledge as a cognitive activity explicable in terms of neural, or more broadly biological, processes. This is a significant departure from the more traditional conceptualisation, favoured, for example, by the logical empiricists, which treats knowledge as an abstract body of concepts tied to evidence by rules of logic. One important consequence of this naturalisation of epistemology is that it makes the distinction between contexts of discovery and justification, what Paul Hoynigen-Huene calls a distinction between the descriptive and the normative, more difficult to maintain [Hoyningen-Huene 1987]. The benefits of this consequence can be seen in Paul Thagard’s neurocomputational model of emotional consciousness. On Thagard’s account, the descriptive and the normative are “closely intertwined”: “[e]ven the acceptance of hypotheses, not just their discovery, has an emotional component” [Thagard 2000, 214]. In this way, the descriptive and the normative considerations, which were clearly and decisively separated in the context distinction, are brought much closer together. Naturalistic epistemology bases its normative considerations, in part, on the way thinking actually

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works. Scientific descriptions of how we reason influence the naturalistic epistemologist’s prescriptions for how we ought to reason.

15 James McAllister appears to also throw his hat in with the naturalists when he argues that scientists’ emotional responses may serve as “reliable detectors of desirable cognitive properties of empirical findings and theories” [McAllister 2005, 571]. Indeed, he cites as one promising example of such a reliable detector Thagard’s model of emotional coherence. I want to now suggest that the epistemic reliability of the natural mechanisms discussed by Damasio, de Sousa, and Thagard might be best treated in terms of a kind of naturalised epistemology called “process reliabilism”. Process reliabilists argue that a belief is justified if it has been formed through a reliable process. According to Alvin Goldman, reliable processes may include such things as standard perceptual processes, remembering, good reasoning, and introspection [Goldman 2009]. The reliabilist thus understands knowledge largely in terms of the processes by which it is formed. She focuses, in other words, on knowledge as a cognitive process rather than as a formal system of beliefs.

16 A reliabilist account of scientific reasoning would thus seem able to accommodate an epistemic role for emotion. The important point here is that, on this account, emotion is conceptualised in wholly naturalistic terms. As a consequence, the logical empiricists’ worry, that emotion is a metaphysical phenomenon incompatible with an empirical conception of scientific knowledge, loses its original force.

4 Scientific emotions as social phenomena

17 A second related worry is that an account of scientific reasoning which incorporates emotions will underwrite an individualistic theory of justification. If this were the case, then it would cut against the commitment of both the logical empiricists and Kuhnians to a theory of justification grounded in intersubjective agreement. It appears that process reliabilism cannot answer this worry. Indeed, as Sandy Goldberg has recently argued, Goldman’s process reliabilism seems heavily biased towards the individual subject, and he suggests instead that the reliability of a belief may also depend on the “prevailing social environment” in which it is formed [Goldberg 2010, 2]. Robert Brandom has made an even stronger claim, arguing that reliability is always intersubjective: [r]eliabilism points to the fundamental social and interpersonal articulation of the practices of reason giving and reason assessing within which questions of who has knowledge arise. [Brandom 1998, 390]

18 If these criticisms of Goldman’s original account are valid, then it would appear that process reliabilism, as a properly naturalistic epistemology, should base its considerations not only on the categories of empirical psychology, but also on those of empirical sociology. As much would seem suggested in Thagard’s admission that he knows of no psychological way of distinguishing between the reliable emotion-based evaluations of a scientist, on the one hand, and her subjective “self-promotion”, on the other [Thagard 2006, 256]. By following Goldberg in modifying orthodox reliabilism, in order to accommodate the insights of social epistemology, we might then argue that epistemic emotions are intersubjective phenomena. As Thagard argues, it is only by working together that scientists will “converge on evaluations [...] that produce a shared reaction of emotional coherence” [Thagard 20 01, 367]. If this synthesis of

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process reliabilism and social epistemology were to succeed, then we would have the basis for an intersubjective account of epistemic emotion. This would then provide us with an answer to the second worry shared by the logical empiricists and Kuhnians, that a recognition of an epistemic role for emotion vis-à-vis scientific reasoning would underwrite an individualistic, or subjectivist, theory of justification. Moreover, the proposed intersubjective account of emotions would also allow us to reconnect with, and perhaps even to vindicate, earlier work on epistemic emotions by feminist epistemologists and philosophers of science like Evelyn Fox Keller, Helen Longino and Alison Jagger. Recall Jagger’s statement, in 1989, that certain emotional attitudes are involved on a deep level in all observation, in the intersubjectively verified and supposedly dispassionate observations of science as well as in the common perceptions of daily life. [Jagger 1989, 189]

5 Conclusion

19 Allow me to now sum up these admittedly tentative remarks. I have sought to answer the question of why philosophers of science have generally turned a blind eye to the epistemic importance of emotion, even though this importance is being increasingly recognised in other fields. One reason for this neglect, I have suggested, is the continuing influence of the historic distinction between the contexts of discovery and justification. Philosophers of science occupy themselves with matters of justification, and they have traditionally dismissed emotion as relevant only to matters of discovery. Yet this dismissal of emotion has been motivated in significant part by a conception of knowledge which is no longer as compelling as it once had been. Process reliabilists, for example, have effectively challenged a view of science as constituted by a formal system of empirically grounded beliefs and rules, and developed powerful tools for exploring it instead as a cognitive, and even historical, process. I have suggested that the reliabilist’s tools, particularly once further sharpened on the stone of social epistemology, offer one attractive point-of-entry into the exciting and still largely unexplored problem-space opened up by the striking possibility that succesful scientific reasoning necessarily depends on the presence in the research process of intersubjectively stabilised epistemic emotions.

BIBLIOGRAPHY

BRANDOM, Robert B. [1998], Insights and blindspots of reliabilism, Monist, 81(3), 371–392.

CARNAP, Rudolf [1928], The Logical Structure of the World and Pseudoproblems in Philosophy, Chicago: Open Court, 2003.

DAMASIO, Antonio R. [1994], Descartes’ Error: Emotion, Reason, and the Human Brain, New York: Putnam Books.

DE SOUSA, Ronald [1987], The Rationality of Emotion, Cambridge, MA: MIT Press.

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GOLDBERG, Sanford [2010], Relying on Others: An Essay in Epistemology, Oxford: Oxford University Press.

GOLDMAN, Alvin [2009], Reliabilism, The Stanford Encyclopedia of Philosophy, E. Zalta, URL http:// plato.stanford.edu/archives/fall2009/ entries/reliabilism/.

HOYNINGEN-HUENE, Paul [1987], Context of discovery and context of justification, Studies in History and Philosophy of Science – Part A, 18(4), 501–515, http://dx.doi.org/10.1016/0039-3681(87)90005-7.

JAGGER, Alison M. [1989], Love and knowledge: Emotion in feminist epistemology, in: Women, Knowledge, and Reality: Explorations in Feminist Philosophy, edited by A. Garry & M. Pearsall, Boston: Unwin Hyman, 129–155.

KELLER, Evelyn Fox [1983], A Feeling for the Organism: The Life and Work of Barbara McClintock, San Francisco: W. H. Freeman.

KOCHAN, Jeff [2013], Subjectivity and emotion in scientific research, Studies in History and Philosophy of Science – Part A, 44(3), 354–362, http://dx.doi.org/10.1016/j.shpsa.2013.05.003.

KUHN, Thomas S. [1962], The Structure of Scientific Revolutions, Chicago: University of Chicago Press, 3rd edn., 1996.

LONGINO, Helen E. [1993], Subject, power, and knowledge: Description and prescription in feminist philosophies of science, in: Feminist Epistemologies, edited by L. Alcoff & E. Potter, London: Routledge, 101–120.

MCALLISTER, James W. [2002], Recent work on aesthetics of science, International Studies in the Philosophy of Science, 16(1), 7–11, http://dx.doi.org/10.1080/02698590120118783.

—— [2005], Emotion, rationality, and decision making in science, in: Logic, Methodology, and Philosophy of Science: Proceedings of the Twelfth International Congress, edited by P. Hájek, L. Valdés- Villanueva, & Westerståhl, London: College Publications, 559–576.

OSBECK, Lisa M. & NERSESSIAN, Nancy J. [2011], Affective problem solving: Emotion in research practice, Mind & Society, 10(1), 57–78, http://dx.doi.org/10.1007/s11299-010-0074-1.

—— [2013], Beyond motivation and metaphor: ‘Scientific passions’ and anthropomorphism, in: EPSA 11: Perspectives and Foundational Problems in Philosophy of Science, edited by V. Karakostas & D. Dieks, Dordecht: Springer, 455–466.

POLANYI, Michael [1958], Personal Knowledge: Toward a Post-Critical Philosophy, Chicago: University of Chicago Press.

RICHARDSON, Alan [2006], Freedom in a scientific society: Reading the context of Reichenbach’s contexts, in: Revisiting Discovery and Justification, edited by J. Schickore & F. Steinle, Dordecht: Springer, 41–54.

THAGARD, Paul [2000], Coherence in Thought and Action, Cambridge, MA: MIT Press.

—— [2001], How to make decisions: Coherence, emotion, and practical inference, in: Varieties of Practical Reasoning, edited by E. Millgram, Cambridge, MA: MIT Press, 355–371.

—— [2006], Critique of emotional reason, in: Hot Thought: Mechanisms and Applications of Emotional Cognition, Cambridge, MA: MIT Press, 251–262.

VIENNA CIRCLE [1929], The Scientific Conception of the World: The Vienna Circle, in: Philosophy of Technology: The Technological Condition: An Anthology, edited by R. C. Scharff & V. Dusek, Oxford: Blackwell, 86–95.

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ABSTRACTS

Recent empirical and philosophical research challenges the view that reason and emotion necessarily conflict with one another. Philosophers of science have, however, been slow in responding to this research. I argue that they continue to exclude emotion from their models of scientific reasoning because they typically see emotion as belonging to the context of discovery rather than of justification. I suggest, however, that recent work in epistemology challenges the authority usually granted the context distinction, taking reliabilism as my example. Emotion may be seen as playing a reliable role in the formation, which for the reliabilist also means the justification of scientific beliefs.

La recherche empirique et philosophique récente remet en question l’idée selon laquelle raison et émotion sont nécessairement en conflit l’une avec l’autre. Pourtant, les philosophes des sciences ont été lents à réagir à cette recherche. Je soutiens qu’ils continuent à exclure l’émotion de leurs modèles du raisonnement scientifique, parce qu’ils considèrent qu’elle appartient typiquement au contexte de découverte plutôt qu’au contexte de justification. Je suggère toutefois, en prenant pour exemple le fiabilisme, que des travaux récents en épistémologie remettent en cause l’autorité généralement accordée à la distinction entre ces contextes. On peut considérer que l’émotion joue un rôle fiable dans la formation des croyances scientifiques, ce qui pour le fiabiliste signifie également leur justification.

AUTHOR

JEFF KOCHAN Zukunftstkolleg – Philosophy, University of Konstanz (Germany)

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The Role of Values in Methodological Controversies: The Case of Risk Assessment

José Luis Luján and Oliver Todt

The research presented in this paper has been supported by the Spanish State Secretary of Research, Development and Innovation’s research projects “La explicación basada en mecanismos en la evaluación de riesgos” (FFI2010-20227/FISO) and “La evaluación de beneficios como ciencia reguladora” (FFI2013-42154), partial funding of which was provided by European Commission FEDER funds.

1 Science and values

1 The relationship between science and values has been articulated in the philosophy of science traditionally by way of asserting an interconnection between cognitive values and scientific change (among others: [McMullin 1983], [Worrall 1988], [Laudan 1984], [Kuhn 1977]). Critics of the notion that cognitive values drive scientific change include many authors related to the fields of cultural studies or the sociology of scientific knowledge who argue that it is the contextual (social) factors that are more relevant (for instance [Barnes 1982], [Knorr-Cetina & Mulkay 1983], [Collins 1983], [Douglas & Wildavsky 1982], [Wynne 1992]).

2 However, another important issue is the relationship between cognitive and non- cognitive values in scientific activity [Machamer & Wolters 2004]. This question is of importance in the applied sciences, and even more in regulatory science (science used for regulatory decision making [Jasanoff 1990]), which will be relevant to our present discussion. The principal issue in regulatory science is that the methodological decisions that appeal to cognitive values can have important social, health and environmental consequences that affect people’s lives.

3 Cognitive values are understood to be those internal to scientific activity itself. These are, for instance, explicative power, accuracy, simplicity, scope, precision, as well as

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internal or external consistency [Kuhn 1977], [Laudan 1984]. Non-cognitive values, on the other hand, refer to the social, political and economic contexts in which scientific activity takes place, as well as the various applications of scientific knowledge (technological products, decision making, public policy, etc.). Examples of such values are operationalization, applicability, robustness, protection of human health and the environment, adaptability, resilience, and controllability [Rudner 1953], [Longino 1990], [Haack 2008], [Douglas 2009], [Todt, Rodríguez Alcázar et al. 2010].

2 Varying perspectives on the role of values in risk assessment

4 In regulatory science, thus, the fundamental question is if regulatory science is different from academic science (driven by cognitive values) and—in case there was a fundamental difference—if non-cognitive values constitute an input for this kind of scientific activity and the knowledge that is generated [Todt & Luján 2014]. For our present discussion the relevant point is that given that academic science is understood to be driven by cognitive values alone [Laudan 1984], while regulatory decision making (and regulatory science itself) may be influenced by non-cognitive values, the question of the relation between the two kinds of values basically is reduced to three possibilities: a) a science-based decision making process driven by cognitive values alone, or b) a process driven exclusively by non-cognitive values, or c) as a third possibility, some kind of interaction between the two types of values in scientific knowledge generation and decision making.

5 An analysis of current science and technology policy controversies with respect to technological risks shows that these are, in fact, directly related to questions of values. In each particular case, different kinds of values (cognitive, non-cognitive) can play varying roles. As a result, an analysis of recent controversies related to precautionary regulation of biotechnology and chemical substances in the European Union (see, for instance [European Commission 2001], [European Parliament and Council 2006], [Todt, Muñoz et al. 2009]) leads us to the following classification of different perspectives on cognitive and non-cognitive values in risk assessment [Luján & Todt 2012]: 1. The Classical Perspective embodies the idea that scientific processes are not to be unduly influenced by non-cognitive values. In practice this means a clear separation of risk management (decision making) and risk assessment (scientific evaluation of risk). The realm of the operation of cognitive values is knowledge generation and justification. No non- cognitive values must exert any influence here. Non-cognitive values, if any, can only be taken into account in decision making. Underlying this perspective is the idea that any scientific uncertainty is the product of a temporary lack of scientific knowledge. Any such currently unavailable knowledge is understood to be able to be generated in the future. In other words, the basis for the assessment of possible future harm from any scientific- technological activity is our currently existing knowledge. 2. Under the Scientific-Technological Trajectories Perspective non-cognitive values turn into the exclusive driving force for decision making. Scientific data about impacts, consequences and risks are considered of secondary importance for decision making. Rather, regulatory decisions consist in identifying technologies (or more commonly, entire technological trajectories) that possess certain “desirable” features (like resilience, diversity, adaptability, reversibility, etc.) that turn them into preferred technological choices. The underlying idea is that technological complexity and the context-dependency of any scientific knowledge

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breeds uncertainty and makes difficult or impossible any control. Certain technological trajectories are considered to possess an inherent capacity for harm, and therefore would have to be deselected. 3. The Methodological Decisions Perspective is based on the recognition that in scientific practice non-cognitive values are unavoidable and exert an influence on scientific activity in all stages, from the initial definition of a research project, through the selection of hypotheses, models and research methods, all the way to data analysis. In particular, non- cognitive values may play a role in the determination of fundamental elements of the framework of any research, like the burden of proof, the standards of evidence, and any models of inference. Non-cognitive values make it possible to evaluate the (social, health, environmental, etc.) consequences of scientific uncertainty and establish the required level of evidence. The underlying notion is that scientific knowledge, as well as its generation and justification, are always subject to fundamental epistemological limitations. The knowledge produced in (academic) scientific research is therefore not necessarily useful for decision making. In fact, in order for scientific knowledge to be relevant for regulatory decisions, the process of its very generation (including scientific methodology) has to be adapted in an appropriate way. In practice, under this perspective, regulatory decision making proceeds on the basis of a risk-assessment-type analysis but the ultimate aim of protecting health and the environment (i.e., non-cognitive values) drives the selection of scientific methodologies.

6 Under the classical perspective the scientific knowledge that serves as input for decisions is a product of a cognitive-values-driven scientific process, while the operation of any non-cognitive values is restricted to decision making. Thus, decisions here are dependent upon both types of values (which at no point interact in the process). Under the Scientific-Technological Trajectories perspective, only non- cognitive values play a role: decisions are the product of (non-cognitive) preferences with respect to technological trajectories. However, in the third case, the Methodological Decisions perspective, we find an interplay of both types of values: non- cognitive objectives in decision making (like protection of health and the environment) drive methodological choices for scientific knowledge production.

7 The interaction between cognitive and non-cognitive values makes this third perspective philosophically particularly interesting. The outcomes (decisions) of the process depend on the specific interrelations of the two types of values in each case. We will now try to analyze some of the implications for knowledge generation and decision making of the operation of values, with special consideration for this third perspective.

3 Non-cognitive values under the Methodological Decisions perspective

8 One of the ways to understand the operation of values is through the analysis of the methodological controversies that are common in risk assessment [Luján 2005]. Those controversies help us in evaluating the above mentioned perspectives on the operation of non-cognitive values.1

3.1 Standards of evidence

9 The standards of evidence refer to the level of evidence required in order to be able to accept an hypothesis. There are two principal controversies here: the first one concerns the question if the standards of evidence that are demanded in risk

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assessment can be considered sufficiently rigorous or not; the second one concerns the type of evidence that has to be taken into account as proof of, for instance, possible negative effects of a substance on human health and/or the environment. As we will see, both issues are intimately related.

10 Some authors argue that the current standards of evidence that are applied to regulatory processes are too demanding [Cranor 2011]. This means, for instance, that possibly toxic chemical substances are currently on the market, even in large numbers, because it has not been possible to show that they are dangerous in accordance with the employed standards of evidence. Consequently, authors like Cranor propose to relax such standards of evidence with the explicit aim of better protecting health and the environment. Relaxing the standards of evidence a) could force a large number of substances that currently are not regulated to be included under existing regulation, and b) would make it possible to evaluate a much larger number of substances with the same basic resources available today (particularly in terms of costs and time). Both effects are considered desirable from the point of view of protecting health and the environment.

11 In order to better assess the role of values we will now analyze two current proposals for methodological change in risk assessment, both of which are directly related to changing the standards of evidence: the weight of evidence approach, and short-term tests.

Weight of evidence approach

12 The weight of evidence approach is a methodology that is based on the idea of taking into account all the scientific information available—from all kinds of different sources and produced according to a diversity of standards—about the possible relationship between a chemical or other substance and health or environmental problems that have cropped up. While it is likely that one single type of information is not sufficient to establish any cause-effect relationships between substance and impacts, all the available information, in its entirety, may allow for taking regulatory decisions. As can be seen, in practice this amount to a relaxation of the standards of evidence, because decisions are not based on one single, isolated piece of evidence (for instance, one particular epidemiological study) but rather on all the respective scientific data as a whole (for instance, studies done at universities, industry, etc., with methodologies ranging from bio-essays to computer simulations, and funded by different sources).

13 Susan Haack argues for the validity of the weight of evidence approach in that the whole of the evidence may be able to better justify a hypothesis than any of its individual components separately [Haack 2008].2 Her argument is based on: • supportiveness: how strong is the connection between the evidence and a specific conclusion. For instance, combining evidence about the biological functioning of a substance with epidemiological evidence, however feeble, results in the whole of the evidence being more supportive of the hypothesis, and increases the amount of available evidence with respect to the possible evidence. • independent security: the degree to which the evidence is solid with independence of the conclusion. Again, as in the previous example, combining evidence about the biological functioning of a substance with epidemiological evidence, however feeble, means that we can be more certain of each of the individual lines of evidence.

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• comprehensiveness: how much of the relevant evidence is incorporated in the conclusions.

Short-term tests

14 Cranor proposes the methodology of short-term tests, particularly for the regulation of chemical substances that are potentially carcinogenic (the tests are focused on aspects like mutagenicity or genotoxicity) [Cranor 1997]. In practice, such short-term tests would consist of in-vitro assays with biological systems (excluding animals), whose duration could be as short as only a few hours (meaning a dramatic improvement over traditional methods which in the case of epidemiological studies may take years to be completed).

15 Cranor’s idea is to substitute, at least in specific cases, short-term tests for bio-assays and epidemiological studies (both of which are, of course, much more time and resource intensive). The need for resources is directly linked to the question of false positives and false negatives. The higher concern for false positives in academic science (which forms the basis of traditional bio-assays or epidemiological studies) is a methodological translation of a cognitive value, namely accuracy.

16 The practical problem in regulatory science is that the predominant concern with false positives leads to a demand for a specific kind of evidence in order to be able to state the toxicity of a substance. Establishing causal connections and trajectories in toxic chemicals is particularly difficult, and the epistemic characteristics of typical academic research about risks associated with toxic substances result precisely in a demand for knowledge about those causal connections and trajectories. As can be appreciated, the combination of both factors results in time and resource intensive research. However, for risk assessment this means that because of the resulting inevitable delays in the availability of data for decision making, there will be an acute conflict between, on the one hand, the cognitive value accuracy and, on the other, non-cognitive values, like protection of human health or the environment.

3.2 Burden of proof

17 The burden of proof has traditionally fallen on the side of governmental regulatory agencies, meaning that they would be the ones to have to demonstrate the harmfulness of a certain product or process in order to be able to justify regulating it. One exception to this rule has been the regulation of pharmaceutical products.

18 However, of late stakeholders (like environmentalists) have been demanding the establishment of a type of pre-commercialization regulation that is based on a shifting of the burden of proof to the producer; meaning that it would be those who are promoting a scientific-technological innovation who would have to demonstrate that it does not entail any major risks for public health or the environment.3 The underlying argument for shifting the burden of proof in this way is that it is concomitant to minimizing false positives. An important moral argument to back up this stance is that those who reap most of the (economic) benefits of the introduction of a new scientific- technological product or process (i.e., its promoters) would have the moral responsibility for demonstrating that they are not generating any important new risks for all other stakeholders. Equally relevant is the empirical argument that states that the current situation under which the burden of proof falls on the side of the public administration (which would have to show that the proposed innovation entails risks

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before being able to justify regulating it) has not sufficiently protected public health nor the environment [Harremoës, Gee et al. 2002].

19 A recent example of the introduction in regulatory practice of the shifting of the burden of proof onto industry is provided by the European regulation of chemical products, REACH (Registration, Evaluation and Authorization of Chemical Substances) [European Parliament and Council 2006].The REACH directive constitutes a shifting of the burden of proof by way of the application of the precautionary principle: a large number of existing (and future) chemicals, the majority of which have never been subjected to any tests, will have to be evaluated for negative health or environmental effects, as a precautionary measure.

4 Conclusions

20 Our analysis demonstrates that in risk assessment methodological value judgments are inevitable and ubiquitous, have multiple important functions, and possess the capacity for considerably influencing or directly determining the outcomes (research results). This is a situation that has to be taken into account not only in risk assessment (generation of knowledge), but also in risk management (decision making).

21 Particularly the proposals of shifting the burden of proof to the promoter of a product or process appeal to non-cognitive values related to the social costs of the different types of errors (false positives or false negatives). Shifting the burden of proof allows for a non-cognitive value like protection of health and the environment to exert an influence on scientific research without compromising its epistemic integrity [Cranor 2011], [Shrader-Frechette 2004], [Wandall 2004]. That is because shifting the burden of proof ensures the generation of fewer false negatives, which in turn leads to a better protection of health and the environment (by minimizing the cases of, e.g., dangerous chemical substances that remain unregulated). This idea is compatible—among the three perspectives presented in section 2—with the Methodological Decisions Perspective.

22 There are other authors (for instance [Koch & Ashford 2006]) who recur to a radical interpretation of the precautionary principle to argue for a shifting of the burden of proof that would force the substitution of chemical or other products that may pose a risk to health and the environment by alternatives that are considered safer, modifying in this way entire technological trajectories. This proposal would fall under the Scientific-Technological Trajectories Perspective.

23 Laudan considers that by the burden of proof before generating any data would be concomitant to a restriction of scientific research [Laudan 2008]. For this author, the relevant question is if a hypothesis, on the basis of the available evidence, has a higher probability than others. In this sense, for Laudan, there is no difference between academic and applied research, in considering both a question of belief. In other words, any moral or political considerations with respect to regulation would always have to be elucidated after data generation, i.e., in decision making. This stance is an example of the Classical Perspective.

24 As to the nature of the standards of evidence, the Classical and the Methodological Decisions Perspectives coincide in considering them theproduct of the interaction between cognitive and non-cognitive values. The decisive difference between the two

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perspectives is that for the Classical Perspective these standards of evidence are simply not part of risk assessment, but rather of risk management (regulatory decision making) [Laudan 2014], while for the Methodological Decisions Perspective they are part of risk assessment [Douglas 2009].

25 For Laudan the standards of evidence are always artificial restrictions imposed on scientific research [Laudan 2014]. This leads him to argue for the abandonment of any such standards of evidence. Laudan’s stance is based on an argument defended by Jeffrey [Jeffrey 1956]: the objective of scientific work does not consist in accepting or rejecting hypothesis, but rather in establishing—by taking into account the evidence available in each moment—its degree of confirmation [Wilholt 2009]. The evaluation of possible consequences of acting (or not acting) upon the hypothesis is a question that is not raised in the risk assessment phase, but only afterwards. What Laudan (as well as other authors [Mitchell 2004]) are arguing for, in the end, is a strict separation of the reasons for belief and the reasons for action. There always exist situations in which one can have reasons to consider more likely a particular hypothesis (rather than its alternatives), while at the same time—and out of caution—not running the risk of acting on the basis of this belief.

26 However, in the light of our discussion, this stance can be considered a very limited one. As we have already seen, non-cognitive values can influence the development of research methodologies in risk assessment. Limiting the function of non-cognitive values to risk management makes it impossible to allow for this methodological improvement [Todt & Luján 2008].

27 Our analysis of the proposals in those two fields, standards of evidence and burden of proof, shows that those proposals can be considered to form part of the context of discovery. The interesting point in relation with the standards of evidence is that methodological proposals like the weight of evidence approach or short-term tests are only viable if we previously accept changes with respect to the standards of evidence (context of justification). In other words, the non-cognitive values are driving a change in the cognitive values which then leads to methodological change in risk assessment. We are, thus, faced with a clear interaction of both kinds of values, cognitive and non- cognitive ones.

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NOTES

1. One area of controversy concerns inference guidelines. These are important because the two principal classical methodologies used in risk assessment, epidemiological studies and bio-essays, are riddled with methodological indeterminacies that make it necessary to extrapolate from the available data to real-world exposure scenarios (usually situations of long term and very low dose exposures, compared to the higher doses and shorter time spans in typical risk studies). Regulatory agencies publish guidelines which explicitly propose certain rules of inference according to the substances under scrutiny [Cranor 1994]. We will not treat this topic here in

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detail because the influence of non-cognitive values in the decisions on what rules of inference to adopt is more or less accepted by all stakeholders. 2. The weight of evidence approach can also be evaluated in relation to a cognitive value like “robustness”. Following this argument, the combination of various and independent lines of evidence increases the robustness in the sense that “truth” would be the intersection of a number of “partial truths”. 3. It is important to point out that in a strict sense it is not possible to shift the burden of proof in this sense, because it would simply be impossible to statistically prove that a scientific- technological product or activity does not suppose any risk for the environment or for human health. Thus, the meaning of the term in the regulatory context is that whoever is promoting an innovation would be bound by law to show that it does not entail any risks, always with respect to a previously established definition of harm [Klinke, Dreyer et al. 2006].

ABSTRACTS

The debate on the role of values in science has also cropped up in the applied science and, particularly, regulatory science. We propose an analysis, from the perspective of values, of the recent controversies related to the role of scientific knowledge in the regulation of technological risks. We differentiate three perspectives on cognitive and non-cognitive values in the context of assessing and managing risk. Our analysis shows that both kinds of values interact in the process of knowledge generation in regulatory science, and that proposals for methodological changes are dependent upon the explicit recognition of the operation of values. Our contribution indicates that the philosophical analysis of values can help clarify the current controversies related to technological risks.

Le débat sur le rôle des valeurs en science survient également dans les sciences appliquées, en particulier dans les sciences régulatives. Nous proposons une analyse, sous l’angle des valeurs, des controverses récentes sur le rôle de la connaissance scientifique dans la régulation des risques technologiques. Nous distinguons trois perspectives sur les valeurs cognitives et non- cognitives, dans le contexte de l’évaluation et de la gestion du risque. Notre analyse montre que les deux types de valeurs interagissent au sein du processus de génération de connaissances dans les sciences régulatives, et que des propositions de changements méthodologiques dépendent de la reconnaissance explicite du rôle opérant des valeurs. Notre contribution indique que l’analyse philosophique des valeurs peut aider à clarifier les controverses actuelles sur les risques technologiques.

AUTHORS

JOSÉ LUIS LUJÁN University of the Balearic Islands (Spain)

OLIVER TODT University of the Balearic Islands (Spain)

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Science-based Metaphysics: On Some Recent Anti-metaphysical Claims

Matteo Morganti

1 Introduction

1 That there is no sharp divide between science and scientific method on the one hand and philosophy and a priori reasoning on the other is quite often reported as an established fact. Interestingly enough, however, the opposition between supporters and detractors of metaphysics survives today more or less in the form imposed by neopositivists, i.e., as a divergence with respect to the alleged fact that metaphysics lacks the “connection” with reality that science, instead, undisputedly possesses. True, many claims for and against metaphysics have been recently made from a renovated empiricist perspective, now free from the constraints set by unworkable criteria of meaningfulness based on direct access and verifiability, and which aims instead (quite sensibly) to make philosophy aware of the results of science. Nonetheless, a shared basis of explicit assumptions and definitions remains absent. It is therefore not surprising that the contenders have been so far unable to truly solve the problematic tension, even in the restricted domain that seems to qualify as “naturalistic” philosophy (more on which in a moment). Something that deserves to be mentioned in this connection, in particular, is that metaphysics seems to have been defined only implicitly, via a loose and vague reference to traditional schools and historical figures in philosophy; and the same holds for the very concept of naturalistic, science-based philosophical methodology.

2 In view of the foregoing, it seems obvious that both enemies and friends of metaphysics should, first of all, seek to better define their views and present sharper arguments in favour of them. In this paper, a small attempt in this sense will be made from a metaphysics-friendly, yet naturalistically-inclined, viewpoint. More specifically, without entering into the larger, and more impervious, domain constituted by issues of

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demarcation and naturalistic methodology in general, the present essay will look at some specific objections that have been recently formulated against metaphysics from the empiricist perspective—Bas Van Fraassen being the primary target. In doing so, some widespread presuppositions will be identified which are, as a matter of fact, more problematic than critics of traditional analytic metaphysics seem to believe. At the same time, the need to re-think metaphysics itself, and make it more continuous with science, will be acknowledged and elaborated upon. Indeed, the discussion of certain anti-metaphysical positions and claims will represent the starting point for a (necessarily partial and provisional) definition of what one might call “constructive” or “liberal” naturalism—the latter being the form of naturalism whereby the continuity between science and philosophy is forcefully upheld and implemented, without ipso facto endorsing any form of eliminativism or strong reductionism with respect to metaphysics itself.

2 Naturalism

3 Very generally put, a naturalistic approach to philosophy and its sub-disciplines consists in seeking continuity between philosophy and science. In practice, there are various ways to understand this and translate it into something more specific.

4 On some construals, for instance, the idea that all knowledge comes from the empirical domain and its treatment via the scientific method leads directly to eliminativism with respect to metaphysics. The idea is simple: if empirical observation and direct testing are necessary for genuine knowledge, only entities, processes and mechanisms posited by science should be taken seriously; therefore, philosophical analysis cannot add anything to science. So understood, then, naturalism leads more or less straightforwardly to a radical form of methodological and ontological reductionism—so radical that it eliminates non-science in favour of science. Other approaches are not eliminativist, but nevertheless recommend a form of reductionism given which metaphysics turns out to be little more than the mechanical extractions of (allegedly) metaphysical claims from scientific theories. Here, the thought seems to be that there is in fact more to scientific theories than their “immediate ontology” (i.e., the theoretical entities that play a direct role in the explanations that the theories provide based on empirical inquiry), but whatever one adds to that is in any case to be “read off” from, and motivated on the basis of, science itself. In this case, if preserved at all, the autonomy of ontological categories and philosophical methodology is, obviously enough, severely limited.

5 Prima facie, no other options are available. Indeed, on the basis of this, some came to believe that naturalism is ultimately a non-starter when it comes to philosophy: for, either it consists in the acceptance of the priority of science at the level of ontology and methodology—but then one is led to the sort of “scientism” just discussed, which entails either reductionism or eliminativism and, consequently, that philosophy plays no real role any longer; or, alternatively, it is maintained that one’s ontology and methodology need not be reduced to those of science, but then one is not a full-blown naturalist, as the sought continuity with science appears to vanish. Of course, this latter option would be acceptable for supporters of traditional analytic metaphysics. It is equally clear, though, that it would at the same time undermine the project of a science-oriented metaphysics. But the very general thought behind naturalism, that is,

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that philosophy cannot be completely separated from and independent of empirical science, seems hard to object to. Hence, one seems to be at an impasse, unable to skirt the above dilemma between too-radical-naturalism and non-naturalism.

6 It is, however, possible to endorse and defend a third-way, a form of “constructive” or “liberal” naturalism that—while rejecting the possibility of acquiring knowledge about the material world via exclusively a priori methods and ruling out everything that may count as “supernatural”—avoids the absorption of philosophy (and metaphysics in particular) by science. Or so it will be suggested here. This will be done based on the idea that, essentially, the constructive naturalist “just” has to separate the request for continuity from the idea that there should be only one methodology and one ontology. What remains of naturalism under such a construal is the idea that all knowledge of reality does indeed come from experience and certainly has to be evaluated against the tribunal of experience. Room is left, however, for an elaboration and construction of such knowledge that goes beyond what can be gathered “mechanically” from scientific theories, and that conceives it as not entirely of an a posteriori nature. Of course, the articulation of such a form of naturalism requires a lot of work, and the discussion of a number of issues that cannot be dealt with in the space of a short paper. What is certainly crucial for the defender of metaphysics, though, is the need to provide compelling answers to certain overtly anti-metaphysical claims and objections that have been formulated in the more or less recent literature, and that seem to convey at least some of the basic ideas underlying radical naturalism. By so doing, it is hoped, any further work in favour of a more sophisticated naturalism will be made easier. This is, then, the limited task of the rest of the present essay (for a more extensive treatment, I allow myself to forward the reader to my [Morganti 2013]).

3 Objections

7 Here are a few objections recently moved against metaphysics.

8 Remoteness. Van Fraassen argues that their remoteness from empirical considerations makes metaphysical questions not meaningless but certainly useless [Van Fraassen 2002]. He notes that science is constantly and harshly tested, and often falsified, but this doesn’t affect, but rather grounds, its practical relevance; while metaphysics seeks the truth, but is never in a position to establish whether what it says is actually true or false, and therefore turns out to be a merely formal exercise.

9 Vacuity. Additionally, Van Fraassen claims that metaphysical questions are irredeemably context-dependent and such that they lack well-defined “answering strategies”. He uses the example of the question “Does the world exist?”; others (see, for instance, Putnam’s discussion of the mereology-related question “How many objects are there in a universe with only three particles?” [Putnam 2004]) offer similar examples.

10 Obscurity. A connected objection made by Van Fraassen is that metaphysics accounts for “what we initially understand [in terms of …] something hardly anyone understands” [Van Fraassen 2002, 3], and consequently turns out to be a superfluous addition to the indications coming fromempirical science.

11 Modality. Ladyman & Ross support their own form of radically reductive naturalism by claiming, among other things, that philosophers have often been wrong in deeming

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something possible or impossible, and it is thus best to learn directly from scientists [Ladyman & Ross 2007]. Relatedly, Callender also laments the lack of a clear definition of the sui generis conceptual space that metaphysics is supposedly concerned with [Callender 2011], supporting instead the view that it is ultimately physical modality that determines what we regard as metaphysically possible, necessary or impossible (this directly relates to claims such as Leeds’ [Leeds 2007], who argues that physically possible worlds are all the possible worlds that there are).

12 These four expressions of scepticism with respect to metaphysics clearly converge towards a deflationary form of naturalism, whereby a priori metaphysical inquiry looses relevance. The resulting perspective meshes perfectly with Van Fraassen’s constructive empiricist attitude. Since s/he doesn’t attach any truth value to any claim about what is not observable (or, at any rate, accessible by empirical means in a sufficiently direct way—the notion ofobservability and the observable/unobservable dichotomy are notoriously problematic) already in the case of undisputedly scientific claims and hypotheses, the constructive empiricist will a fortiori take all claims about, say, universals or object-stages as not even worth thinking about. Notice, however, that realists (Ladyman, Ross, and Callender seem to qualify, and see themselves, as such; perhaps Putnam too, even though in his case the story is more complicated) can go in a similar direction. For, they can take questions about unobservable entities and their existence seriously, but be at the same time committed to the existence of some unobservables only. More specifically, they can draw a principled distinction between scientific unobservable posits and metaphysical unobservable posits, and systematically demote the latter to the role of mere by-products of intellectual games that have no connection whatsoever with reality.

13 What can defenders of analytic metaphysics say about this? What can they do in order to resist the above charges? How is a more liberal and comprehensive form of naturalism to be defended? Here are some suggestions.

14 Remoteness appears far from conclusive. In particular, since it informs the interpretation of science, metaphysics is in a sense at least indirectly testable, i.e., it is not entirely immune to, and indifferent towards, the empirical input. Consider, for instance, the issue concerning the (non-)individuality of quantum particles, crucial in the context of the interpretation of quantum theories, non-relativistic quantum mechanics in particular. To be sure, quantum theory tells us things that are fundamental for establishing (or at any rate making conjectures about) what reality is like, and thus what sorts of entities there really are “out there” and what sort of identity conditions they exhibit. But this empirical/theoretical input does not give us any well-defined, conclusive indication with respect to the issue at hand. Any analysis aiming to tell us what the entities quantum mechanics is about really are, and whether these qualify as individuals more or less in the same way as their classical counterparts do or instead call for radical conceptual revision, will have to rely more or less implicitly on extra-scientific assumptions—“extra-scientific” meaning here that these assumptions can only be spelled out in philosophical terms, not in the vocabulary of physical theory. And it is here that what we called “indirect testability” kicks in. Think, for instance, of properties and the infamous “problem of universals” in metaphysics. Realists about universals who do not also postulate substrata/bare particulars are (more or less—we will avoid discussing the details here) compelled to endorse Leibniz’s principle of the Identity of Indiscernibles. But the latter is exactly what seems to be put

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into doubt by quantum mechanics: the physical world appears to be such that there are numerically distinct physical systems with all the same properties. In reaction to this, one might then try to modify the Leibnizian approach to individuality, or have recourse to different ontological frameworks (say, with tropes rather than universals, or bare particulars, or primitive identities). It is, thus, metaphysical categories that inform our interpretation of the theory. In this connection, two crucial points must be made explicit: first, as the above case of the advent of quantum physics and of realism about universals shows, metaphysical conjectures and theories can turn into empirically relevant theses—at least in the sense that they become indirectly testable, i.e., relevant for the interpretation of science, at specific junctures in the history of science (and philosophy); secondly, even in this setting it is not (normally) the case that science provides univocal indications as to what metaphysical system provides the right interpretation, and thus “philosophers should just listen to scientists”. Rather, the comparison of the various possible interpretations is itself a non-mechanical, purely philosophical process—one which involves a consideration of pragmatic virtues, the definition of criteria for theory-choice, the comparison of different hypotheses and explanations and so on.

15 If the above is correct, Chakravartty makes a compelling point when he claims that— while a scientific antirealist may coherently refrain from doing metaphysics—scientific realists, or at any rate those who have a serious interest in the interpretation of scientific theories, should not do the same [Chakravartty 2007]. Indeed, strictly speaking, the remoteness objection cannot be neutralised: whether or not one takes metaphysics as an enterprise worth pursuing is just a matter of choosing one’s “stance”. Still, in a realist context (that is, in a context that naturalists certainly cannot rule out and probably regard as default) metaphysics does seem to have an important role to play. And the same goes for the (probably rare in practice, but logically possible) positions that consider the interpretation of our best science relevant and/or philosophically interesting but do not subscribe to scientific realism.

16 Having said this, can aptly naturalised metaphysics be characterised more precisely? Yes: this requires dealing with the other objections listed above. First of all, Vacuity can be answered by pointing out that the detractors of metaphysics usually portray metaphysics as a sort of Quinean search for what exists in a way that need not be regarded as compelling. For instance, Lowe convincingly distinguishes between “bad” (Quinean) metaphysics and good metaphysics [Lowe 2011], and Schaffer compellingly argues that defending metaphysics on the basis of the Quinean view is a non-starter [Schaffer 2009]. The idea is, roughly, that if one is to compile an inventory of what exists it is indeed best to listen to expert scientists. Yet, at least if one doesn’t regard this listing task as primary for metaphysicians, there might be more to say. As for possible alternatives, these authors suggest that metaphysics is essentially a study of possibilities and of dependence relations, respectively. That is, that rather than (or, before) trying to put together a list of the things, or sorts of things, that exist, metaphysicians should aim to individuate possible ways things might be; first and foremost, possible ways in which things might be structured together on the basis of fundamental priority and dependence relations. This is tantamount to saying that existential questions of the Quinean type play only a secondary role. And that answers to them can (and perhaps should) be sought by looking at science, but only provided

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that the latter is “philosophically filtered”, hence interpreted, on the basis of general categories of things that are 1. more encompassing than those of science; 2. essentially provided with the features that account for the priority or dependence of certain facts with respect to others.

17 Consider, for instance, the above example of identity in quantum mechanics: do identity facts depend on qualitative facts, as Leibnizian would have it? Or can the former be autonomous and perhaps more fundamental? It is these, clearly philosophical, questions that turn out to be fundamental for answering questions of interpretation of the relevant physics. And similar questions can be asked with respect to issues concerning composition, persistence, space-time and matter, dispositions and a lot more: most, if not all, of which—it would seem—can be made directly pertinent to the interpretation of actual scientific theories.

18 Going back to the main argument, then, it looks as though, once it is understood in the post-Quinean fashion just sketched, metaphysics can be made immune to the vacuity objection. And that this is so essentially because of what we contended earlier, namely, that by grounding interpretations of scientific theories, metaphysics finds at least an indirect connection with the “empirical input” that is rightly considered fundamental by empiricists/naturalists.

19 Moving on, as for Obscurity, it could be replied to Van Fraassen that scientific theories are not “initially understood”, for they cannot be understood unless interpreted and interpretation, as we argued, requires tools coming from outside of science. Before those tools are applied, at most one has the sort of instrumental ability and knowledge that can only be deemed satisfactory—besides scientists themselves—by thorough antirealists. Of course science doesn’t need philosophy when it comes to building faster rockets or better particle accelerators. But does this really count as understanding? In addition to this, it seems fair to also say that the concepts and categories typical of metaphysics are not (necessarily) obscure, but rather the opposite: for, in general, they follow from a conceptual analysis with respect to questions about reality which is closer to common sense than its scientific counterpart. For instance, is the notion of a universal, say, any more obscure than that of a Higgs boson? The answer is by no means obviously affirmative unless one equates clarity with measurability or something like that. But, again, this is not what one normally intends by “understandability” and “clarity”—not even, notice, in any sensible antirealist context.

20 Getting back to metaphysics as a study of possibilities, and moving on to the Modality objection, Ladyman & Ross’ criticism is not convincing either, as it rests on an ambiguity: true, philosophers have been often wrong in claiming that x is (not/ necessarily) the case; but only the weaker claim is relevant here that metaphysics identifies the range of conceptual possibilities that will have to be evaluated on the basis of our best knowledge of reality, and tells us whether or not x is among these. Only in limiting cases can metaphysicians claim that reality must, or cannot be, conceived of in such and such a way, but this is only to be expected. For, conclusive claims about the way things are can only be reached by a priori means in those realms in which the empirical input is not relevant (e.g., logic, or geometry), or in the rare (if at all conceivable) cases in which all hypotheses except one are internally inconsistent. Thus, even if actual philosophers may have thought and done otherwise, this is the way metaphysics can and should be understood by liberal naturalists: namely as an

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enterprise dealing with possibilities that—so to put it—are not in competition with those identified with the sciences but, rather, are more general than these and, therefore, play an essential preliminary role with respect to them. In connection to this, two interrelated remarks are worth making: 1. Scientific theories too, fallible though they might be, are presented—at least at the popularisation level—as true; scientists too have in this sense been wrong in the past; 2. If fallibility is a positive aspect of science, why not say the same about metaphysics, and instead condemn the latter exclusively on the basis of examples of specific actual philosophers with incorrect opinions?

21 This directly connects to another important point. If metaphysics is not acknowledged as an a priori study of possibilities, this has unwelcome consequences for all forms of strong naturalism that are not coupled with scientific antirealism and eliminativism with respect to metaphysics. For, where do the specific non-scientific claims that those naturalists put forward get support from? For instance, Ladyman & Ross’ own positive metaphysical view (a form of so-called “ontic structural realism”, according to which reality is fundamentally a complex structure of “real relations” with modal weight, and science gradually uncovers such structure) is presented as a direct consequence of our best current science. However, it is undeniable that ontic structural realism is in fact a distinctively philosophical thesis, which is arrived at, and can be argued for and against, via a critical comparison of metaphysical alternatives. But if this is so, then it seems that the work of those “Scholastic” metaphysicians that Ladyman & Ross are eager to get rid of is in fact useful, if not necessary, for scientifically-minded philosophers after all (at least, to repeat, if they want to steer clear of antirealism and instrumentalism, and provide a metaphysical interpretation of scientific theories). For, instead of being inevitably “disconnected from reality”, at least some of the metaphysical constructions that are openly dismissed as uninteresting by detractors of metaphysics (may) turn out to prove able to inform our interpretation of scientific theories, thus being at least indirectly tested against the empirical input in the sense defined earlier. (Quick example: Ladyman & Ross ridicule philosophers talking about “gunk” and infinite layers of ontological dependence, but then claim that it could be the case that “it is relations all the way down”!)

22 The worry remains that, even if an independent set of questions, concepts and methods might be acknowledged that qualifies as metaphysics, physical/nomological modality might be all that counts. However, far from establishing that metaphysics should be eliminated or absorbed by science, this only shows that there might, at root, only be one kind of possibility/necessity in reality. And this sort of monism (or at any rate reduction of metaphysical modality) is by no means sufficient for dispensing with metaphysics altogether. For, it might well be the case that all sorts of possibilities and necessities that play a role in the actual workings of the universe are of the sort inquired into and accessed by empirical science. But this does not mean that it makes no sense and is, in particular, irrelevant for the interpretation of scientific theories whether, say, properties are universals or tropes, whether identity facts supervene on qualitative facts, whether Humean Supervenience is true, what ontological status time has, and so on. In other words, whether or not one defends the autonomy and irreducibility of metaphysical modality, one can in any case defend the autonomy and irreducibility of metaphysical discourse (provided, of course, that the latter meets certain methodological requirements). (In connection to this, it must also be mentioned

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that the reduction of metaphysical modality is less straightforward than one may think: Fine, for instance, provides sophisticated arguments against the reduction of the metaphysical and normative modalities to natural modality [Fine 2002].)

4 Methodology

23 We have contended that appropriately naturalised metaphysics must aim to identify possibilities that are—at least potentially—relevant for the interpretation of actual scientific theories, and that are not (merely) compared on the basis of a priori considerations. And we have also suggested that a good way of doing this is by working with general categories and trying to find the mutual relationships of priority and dependence that hold between these. What else can be said in this sense? What principles (if any) can and should guide us in evaluating and selecting metaphysical hypotheses in the light of the indications coming from science, so also providing the most plausible interpretative background for scientific theories themselves?

24 As is well known, criteria for theory-choice in science have long been identified and widely discussed in the past, and it is agreed that they are essentially the following, well-known at least since the work of Kuhn: empirical adequacy, logical consistency, breadth of applicability, simplicity and fruitfulness. In the case of metaphysical theory- choice, prima facie it seems that these criteria can be preserved, albeit with some obvious modifications connected to the fact that one doesn’t have direct testability or unification of independent empirical hypotheses and models but, rather, what we called indirect testability and unification of (at least partly) non-empirical hypotheses and models, respectively. However, there is more to say.

25 First of all, it might be thought that one of the things that are obtained by switching to a naturalistic metaphysics is the possibility to conclusively discard certain metaphysical options, and perhaps regard certain others as certainly correct, based on the empirical data, no matter how close to entrenched beliefs these might be—some think, for instance, that this is the case with presentism based on relativity theory. This would mean that empirical adequacy trumps (or may override) all other factors in a decisive way. However, this is not so—in fact, we have already indirectly questioned this when discussing the example of quantum individuality. Indeed, there is (almost) never a direct relation of logical entailment between a scientific theory and (the negation of) a metaphysical hypothesis. Indeed, this is why we have claimed that metaphysics cannot just be read off from our best science. But if the criterion of compatibility with the empirical data cannot be intended as something with a mechanical application, and, possibly, conclusive “yes” or “no” answers then it must be applied in parallel with the other criteria mentioned above.

26 Without discussing all the criteria one by one, let us say something about one of them in particular. In the above context of theory-comparison and theory-choice at the point of intersection between science and metaphysics, it seems interesting to explore the prospects for a non-naïve criterion of conservation of entrenched beliefs. To be sure, one should not aim for a defence at all costs of commonsense intuition, especially not for the defence based on pseudo-science that Ladyman & Ross believe to be a distinctive mark of most contemporary metaphysics. Rather—without this being tantamount to being conceptually conservative come what may, let alone always trusting less revisionary hypotheses—one might try to construct one’s metaphysics,

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and put metaphysics and physics together, in such a way that the least possible amount of revision is implemented. Indeed, something like the following reasoning seems to hold generally. Since the acceptance of any new hypothesis required for explanation implies acceptance of its consequences, our need for explanation entails acceptance of conflict between old and new beliefs. Therefore, some revision in our web of beliefs is always required. But our aim must be (obviously enough) to eventually obtain a new web of beliefs which is internally consistent and includes the new explanatory hypothesis. And changing as little as possible while obtaining this latter result is not only advisable but almost necessary given the amount of conceptual work needed as well as the fact that new explanations are continuously sought and, consequently, new adjustments and conceptual revisions always required. Hence, we should (and in fact do) aim to minimise conceptual revision based on the available evidence. This way of thinking was openly endorsed, for instance, by the pragmatist William James. According to James: The most violent revolutions in an individual’s beliefs leave most of his old order standing. […] We hold a theory true just in proportion to its success in solving this “problem of maxima and minima” […]. Their influence [that of the older truths] is absolutely controlling. Loyalty to them is the first principle—in most cases it is the only principle. [And …] new opinion counts as “true” just in proportion as it gratifies the individual’s desire to assimilate the novel in his experience to his beliefs in stock. [James 1907, lecture II]

27 Similar ideas about “minimising conceptual revision” have been developed and defended by Quine and Ullian [Quine & Ullian 1978] (a clear elaboration, of course, of Quine’s criterion of “minimal mutilation” of established beliefs).

28 Whatever one thinks of this, let us look at criteria of theory-choice more generally before closing. Evidently, a careful evaluation of all the relevant factors is crucial, and it is not obvious that procedures for precisely quantifying the parameters to be taken into account in order to then compare the various alternatives are available. But why should criteria of theory-choice only be applicable to the extent that their respective weights can be precisely quantified? After all, what we are looking for are some indications for how to carry out the critical evaluation of alternative options. That these criteria should lead to uncontroversial, objective and shared conclusions seems to be an additional request, and failure in this respect doesn’t entail the collapse of the entire project. Indeed, a similar lack of an objective “measure” certainly doesn’t entail —at least not in any obvious and agreed upon way—that talk of pragmatic criteria and theoretical virtues should be given up in the case of scientific theory-choice.

29 An objection might be that one cannot in fact have recourse to theoretical virtues and pragmatic criteria for assessing metaphysical conjectures because metaphysical theories are underdetermined with respect to all possible observations (“strong underdetermination”) and not just all observations (“weak underdetermination”) carried out until now, and thus there is no ground for believing that pursuing theoretical virtues such as simplicity and the likes leads to epistemic improvement in metaphysics. But this would mean to ignore the response suggested above to the remoteness objection. There, we have put a fundamental emphasis on the idea that those theoretical levels which are more abstract and farther away from the evidence and the available/possible empirical data must be supported by being systematically put into relation with other levels, typically scientific ones, which are closer to such data. What this means is exactly that the seemingly strong underdetermination

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besetting metaphysics might (albeit perhaps not in all cases) be shown to be almost as weak as that obtaining in science after all, as conjectures that previously seemed entirely abstract and disconnected from reality (may) turn out to make a difference when it comes to interpreting specific theories. In light of this, it appears sensible to apply to those conjectures the same criteria for theory choice that are employed in the case of plainly scientific hypotheses. After all, what principled way could there be for determining when a given hypothesis is necessarily strongly underdetermined? Wouldn’t one run the risk of making a claim analogous to the claim that, while mathematics is generally useful for the development of physics and so the pursuit of mathematics for its own sake is generally justified, there is a specific bit of mathematics that is in principle useless for, say, physicists? (I think the analogy between metaphysics and mathematics is useful, but there is no space to develop it here).

5 Conclusions

30 Overall, it looks like metaphysicians can and should steer clear of both agnostic/ sceptical empiricism and naively understood naturalised metaphysics by endorsing the following theses: 1. Metaphysics cannot be read off from science; 2. Metaphysics is a priori while science is based on observation and experiment; 3. Both metaphysics and science employ inference to the best explanation and have recourse to pragmatic/theoretical considerations when evaluating competing hypotheses; 4. Metaphysics seeks the most fundamental and general truths, and therefore has to employ peculiar concepts and categories; 5. Metaphysics studies a space of possibilities characterised by dependence and priority relations, (likely to be grounded in the (metaphysical) essences of the (metaphysical) sorts of things being postulated); 6. Metaphysics obtains answers either via pure logical analysis or, much more importantly, via logical analysis plus a consideration of our best current science; 7. Naturalism about metaphysics should be understood as the view that metaphysics should preserve its autonomy but be studied in parallel with science, being put to the test of the empirical evidence while at the same time defining the tools for the interpretation of science itself; 8. Pragmatic criteria of theory choice can and should be employed when it comes to choosing between different ways of putting metaphysics and science together (and this, among other things, may allow for a motivated defence of common sense beliefs).

31 If one adds to this a form of agnosticism about whether or not metaphysical modality is autonomous and irreducible, one obtains at least the sketch of an approach to metaphysics which pays enough attention to science to qualify as naturalist but, at the same time, preserves a degree of autonomy sufficient for avoiding the most radical forms of naturalism and the kinds of criticisms against metaphysics formulated on the basis of them.

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BIBLIOGRAPHY

CALLENDER, Craig [2011], Philosophy of science and metaphysics, in: The Continuum Companion to the Philosophy of Science, edited by S. French & J. Saatsi, London: Continuum, 33–54.

CHAKRAVARTTY, Anjan [2007], A Metaphysics for Scientific Realism: Knowing the Unobservable, Cambridge: Cambridge University Press.

FINE, Kit [2002], The varieties of necessity, in: Conceivability and Possibility, edited by T. Szabo Gendler & J. Hawthorne, Oxford: Oxford University Press, 253–282.

JAMES, William [1907], Pragmatism, A New Name for Some Old Ways of Thinking, Popular Lectures on Philosophy, New York: Longmans, Green and Company, 1979.

LADYMAN, James & ROSS, Don [2007], Every Thing Must Go. Metaphysics Naturalised, Oxford: Oxford University Press, (with Spurrett, David and Collier, John).

LEEDS, Stephen [2007], Physical and metaphysical necessity, Pacific Philosophical Quarterly, 88(4), 458–485, http://dx.doi.org/10.1111/j.1468-0114.2007.00303.x.

LOWE, E.J. [2011], The rationality of metaphysics, Synthese, 178(1), 99–109, http://dx.doi.org/ 10.1007/s11229-009-9514-z.

MORGANTI, Matteo [2013], Combining Science and Metaphysics. Contemporary Physics, Conceptual Revision and Common Sense, Houndmills; Basingstoke: Palgrave Macmillan.

PUTNAM, Hilary [2004], Ethics without Ontology, Cambridge: Harvard University Press.

QUINE, Willard van Orman & ULLIAN, Joseph S. [1978], The Web of Belief, New York: McGraw-Hill.

SCHAFFER, Jonathan [2009], On what grounds what, in: Metametaphysics: New Essays on the Foundations of Ontology, edited by D. Manley, D. Chalmers, & R. Wasserman, Oxford: Oxford University Press, 347–383.

VAN FRAASSEN, Bas [2002], The Empirical Stance, New Haven: Yale University Press.

ABSTRACTS

This paper focuses on the debate concerning whether and, if at all, in what way metaphysics should be accepted alongside science. It examines some recent objections levelled, among others, by Bas Van Fraassen against metaphysics as an intelligible and autonomous enterprise worth pursuing. Replies to these objections are formulated. Science-based metaphysics is then de_ned in some detail, essentially as an a priori study of a possibility space that requires metaphysics to be “fleshed out”, as it were, on the basis of science, but at the same time renders it necessary for the interpretation, and thus proper understanding, of science itself. Crucially, the resulting framework questions the idea that naturalism necessarily entails the elimination of metaphysics or its ontological/methodological reduction to science.

Cet article se concentre sur le débat concernant la question de savoir si et, le cas échéant, de quelle manière la métaphysique doit être acceptée à côté de la science. On examine certaines objections récentes lancées, entre autres, par Bas Van Fraassen, contre la métaphysique entendu comme une entreprise autonome et intelligible digne d’être menée à bien. Des réponses à ces objections sont formulées. On présente ensuite de manière plus détaillée une métaphysique basée

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sur la science: on définit celle-ci essentiellement comme une étude a priori d’un espace de possibilités, ce qui requiert que la métaphysique soit pour ainsi dire « étoffée» sur la base de la science, mais qui la rend en même temps nécessaire pour l’interprétation, et donc la compréhension correcte, de la science elle-même. Le cadre résultant met en question l’idée que le naturalisme implique nécessairement l’élimination de la métaphysique ou sa réduction ontologique/méthodologique à la science.

AUTHOR

MATTEO MORGANTI ‘Roma TRE’ University, Rome (Italy)

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Theory Success: Some Evaluative Clues

María Caamaño-Alegre

1 Preliminary remarks: the disambiguation of “theory success”

1 The starting point of the paper is a distinction between four main, not mutually exclusive kinds of theory success: 1) the one concerning a greater empirical adequacy or fit (oxygen theory versus phlogiston theory, relativistic mechanics versus Newtonian mechanics), 2) that due to an increase in predictive power, which clearly entails a rise in empirically “promising” informativeness (theory of relativity versus Newtonian mechanics), 3) that derived from a higher explanatory capacity accomplished in terms of a more detailed specification of those causal mechanisms underlying the empirical phenomena under study (Mendelian genetics versus theory of the mixture), 4) the one related to a higher explanatory capacity achieved through a more systematized and unified account of empirical phenomena (Newtonian mechanics versus Galilean Mechanics). Theory success of either kind can be understood as a form of explanatory success (predictive, informative, causal, and unitary-systematic respectively), each of them having been historically emphasized from different philosophical standpoints (by authors like K. Hempel, P. Kitcher, M. Friedman, and W. Salmon). This persistent ambiguity surrounding the notions of explanation and success will be avoided here by carefully specifying which side of explanation is being considered. As already said, I am going to focus on the first kind of theory success, which, from the approach adopted here, presupposes also the second kind of success.

2 The above distinction, however, becomes more complicated once we take into account the fact that either kind of theory success may occur in a (conceptually) continuous or discontinuous fashion, depending on whether the successor (more successful) theory is conceptually compatible (or commensurable) with the predecessor (less successful) one. Challenges posed by conceptual discontinuity will be minimized here by assuming T. S. Kuhn’s late notion of local incommensurability [Kuhn 1982, 1983], which allows for

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empirical commensurability and rational comparison between rival theories. The concepts shared or commonly presupposed by incommensurable theories would provide a commensurable ground for theory evaluation.

3 Another point to clarify is the possibility of distinguishing between success due to a theory and success merely accompanying the theory, that is, taking place as the theory develops but not because of the theory. Throughout this paper, the expression “theory success” will refer to that success dependent on the theory under consideration, rather than to that not dependent on such theory but just occurring simultaneously with its development. The example of the caloric theory is often used to show how certain research components are preserved in science. This preservation has been accounted differently depending on whether the adopted approach is realistic or instrumentalist. Authors like S. Psillos, P. Kitcher or J. Worrall, provide a realistic account of the caloric case, claiming that much progress made by the caloric theorists has been preserved by upholders of succeeding theories. According to Psillos, the achievements made during the development of the caloric theory, were the following: the development of calorimetry (specific heat), the law of adiabatic expansion of gases, and Carnot’s theory of heat engines [Psillos 1994]. On the other hand, non-realists like L. Laudan or H. Chang reply by objecting that what is preserved does not include theoretical components but elements that are independent of the caloric theory. In emphasizing the independence of these research constituents, Chang stresses the relevance of the following: observational data, phenomenological laws, non-empirical elements like representational or inferential techniques (including mathematical methods), and deeply rooted metaphysical commitments [Chang 2003, 910-911]. This metaphysical debate on preservation will not be resumed here, since the present focus of discussion is rather the dependence or independence of research achievements with respect to a given theory. Whatever view we hold on this particular case, the interesting point to note here is the very possibility that not all achievements accomplished during the period when a theory is developed are due to the very theory.

4 Finally, questions about whether theory success implies some sort of truth approximation, or whether it provides grounds for a realist conception of scientific theories, are going to be put aside. Since arguments in favour of these ideas are supported on considerations concerning success of the above kinds, clarification of the latter turns out important regardless of what view is hold with respect to the former issues. This metaphysical neutrality extends here over all realist and anti-realist options in the “market”, from entity realism (different versions of which are endorsed by Kitcher, Hacking, and Giere among others) to structural realism (developed by authors like Worrall, Ladyman, French), and anti-realism in its different varieties and degrees (Laudan, van Fraassen, Cartwright).

2 Limitations of traditional approaches to theory success

5 As already pointed out, traditional criteria for theory success mainly revolved around the number of a theory’s successful applications—which, from the statement view of theories [Popper 1962], amounts to the number of a theory’s true empirical consequences, and, from a model-theoretic approach [Moulines 2000], to the number of phenomena successfully embedded into theoretical models through those models’

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empirical substructures. In characterizing a theory (T2) as more successful than

another theory (T1), traditional accounts of theory success (S) have usually committed

to the following, merely quantitative condition: S(T1) ⊂ S(T 2), sometimes supplemented

with the Kuhnian condition that S(T2) includes some of T1’s most recalcitrant anomalies.

6 However, this purely quantitative account of theory success, even if supplemented with the assumption that there is an inter-theoretical epistemic-pragmatic criterion for prioritising certain intentional applications whose possible extension to models is of special interest, is not revealing enough as an analysis of theory success. A major problem has to do with the fact that the requirements placed on the success of competing theories are merely quantitative, and for this reason, insensitive both to the empirical import of the intended applications covered by the theories and to the explanatory significance of the models accounting for the applications. With respect to the first, it is worth mentioning the special relevance given to novel, unexpected predictions or to those concerning salient phenomena which were not initially included in the domain of application of the theories. It seems plausible to think that even if a theory fails to satisfy the condition mentioned in the last paragraph, it could still be considered as more successful than its competitor in case that only the first provided unexpected predictions and an explanation for previously disregarded salient phenomena. Relativity theory may illustrate this kind of success, since it was considered successful, at least partly for these reasons, even before it could be confirmed to the same extent as Newtonian mechanics had been. There can also be cases (like Ptolemaic and Copernican theories) in which rival theories do not differ in their quantitative success, and yet one of them is considered as explanatorily superior to the other. The two conditions above are not applicable here, and yet there seems to be a clear difference in success between the two theories. Before Galileo, Ptolemaic and Copernican astronomy could roughly account for the same phenomena. However, the second was regarded as a better explanation, not only due to its greater simplicity and unifying capacity, but also to its less ad hoc character. A further problem affecting the traditional standpoint concerns the meagre attention paid to the scope, generality or informativeness of a theory as an element of success. In other words, the quantitative requirement can be met without the scope of the theory significantly changing.

7 The above observations suggest that some important questions remain unanswered in traditional accounts of theory success. These questions point to the need for refinements in the form of several qualitative requirements, which should be specially focused on issues regarding a theory’s scope and possible ad-hoc-ness. More in particular, such requirements will concern: a) the resolution of non-refuting anomalies [Laudan 2000, 166-167], b) the superiority of prediction over accommodation [Lipton 1991, 68], and c) the limited use of non-corroborated auxiliary hypotheses [Thagard 1978, 86-89]. Notice the especial relevance that all the above features have to the question of empirical adequacy, and which becomes evident in the fact that a) is directly connected to both empirical adequacy and informativeness; b) is related to informativeness and indirectly to empirical adequacy (possibility of increasing empirical adequacy by increasing informativeness); and c) is indirectly related to the empirical adequacy of a theory, since it is directly related to the empirical adequacy to the theory’s auxiliary hypotheses.

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8 In order to provide an answer to these issues, a stronger notion of empirical adequacy is sketched in the next section.

3 Developing a stronger notion of empirical adequacy

9 In dealing with the problem of theory success, traditional approaches face some serious shortcomings, in particular those related to the neglect of the problems regarding ad- hoc-ness or the insufficient attention paid to issues concerning the application openness or incompleteness of a theory. A stronger notion of empirical adequacy is needed in order to overcome these shortcomings. So next we are going to take into account several hints provided by some of the authors who most seriously attempted to show the significance of the above qualitative requirements. Let us first pay attention to the issue concerning non-refuting anomalies.

10 A) The notion of non-refuting anomaly is introduced by Laudan in Progress and its Problems [Laudan 1977], where he characterizes anomalies in general as “empirical problems which raise reasonable doubts about the empirical adequacy of a theory” once another theory has solved them [Laudan 1977, 28-30]. According to him, non- refuting anomalies, in contrast to refuting ones, do not involve any logical incompatibility between empirical consequences of the theory on the one hand and verified statements regarding empirical facts on the other [Laudan 1977, 27-29]. They rather entail a theory’s incapability to account for certain kinds of salient empirical phenomena whose description is consistent with everything established by the theory. As Laudan puts it: Such non-refuting anomalies typically arise when one theory is compatible with, but offers no solution to (or explanation of), certain phenomena for which some of its rivals can give an account. It was my claim that the scientific methodologies of logical empiricism had not recognized this historically significant form of anomaly. [Laudan 1981, 618]

11 Non-refuting anomalies, therefore, do not primarily point to any mistake on the way in which a theory explains the phenomena but rather to the incompleteness on the part of the theory. Typical cases in which this happens are the ones pointed out by Laudan when developing the notion of non-refuting anomalies in arguing for the importance of completeness as a theoretical virtue. In his work from 1977 he mentions two cases: the incapability of pre-Galilean kinematics to explain the mathematical features of pendular motion, i.e., the absence of predictions for the geometry of the moving weight, and Newtonian mechanics’ lack of explanation for the coplanarity and common direction of the planets’ orbits, which had been accommodated in Keplerian and Cartesian astronomies [Laudan 1977, 29]. Some other examples are added in his 2000 paper; for instance, the fact that continents fit together, for which stable-continent theories of geology offered no explanation, or the phenomenon of residual background radiation, which remained unexplained by steady state cosmology [Laudan 1977, 167].

12 Laudan’s conception of anomalies, strongly inspired by Kuhn’s [Kuhn 1962, 52-65],1 includes the idea that anomalies can only be regarded so when another theory has been capable of solving them.2 Here a wider notion of anomaly is favored instead. According to this wider characterization, anomalies (of either kind) consist in empirical problems that raise rational doubts about the empirical credentials of a theory regardless of whether another theory has succeeded in solving them.

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13 We can already give an idea of what distinguishes non-refuting anomalies from cases where some phenomena remain unexplained by a theory either due to the fact that they fall outside its domain of application or because, despite being included in the domain, it is foreseeable that the theory, as it stands, will be able to account for them in the future. Unlike the first kind of case, non-refuting anomalies have close similarity or connection to paradigmatic exemplars of a theory’s intended applications; as opposed to the second kind of case, these anomalies, because of their recalcitrant nature, suggest that the theory will need substantial modifications, additions or even a replacement. Against this, and favoring Laudan’s view, it could be argued that unless there is a contrast class of alternative theories capable of solving certain non-refuting empirical problems, we do not have grounds for regarding the latter as anomalies rather than just mere problems of adjustment between theory and data, or, alternatively, mere empirical findings not targeted for explanation (even if closely similar to paradigmatic exemplars). In reply to the first option, it must be emphasized that non-refuting anomalies point not to those cases in which a theory speaks only very approximately but to those cases where a theory, despite possible efforts to the contrary, remains silent with respect to certain phenomena. As for the second possibility, it is important to note that anomalies consist in salient or striking phenomena that, given their relevance to the theory, the latter should be able to accommodate.

14 Let us now turn to the most central and insightful aspect in such characterization, i.e., the widening of the evidential or evaluative basis for a theory to embrace verified empirical statements that are neither among the set of the theory’s consequences nor among the set of the theory’s excluded consequences. To use Laudan’s own terms, his discussion of non-refuting anomalies entails the rejection of the “consequentialist theory of evidence or plausibility” [Laudan 1995, 28], as well as the recognition that “[...] being a consequence of a hypothesis is neither necessary nor sufficient to qualify something as evidence for that hypothesis” [Laudan 1995, 29]. The warrant conditions of a statement, therefore, should not be equated with its truth conditions, since poor explanatory power would raise doubts about the epistemic virtue of a theory regardless of whether the latter’s truth conditions are widely satisfied [Laudan 1995, 33].3

15 The empirical adequacy of a theory, then, does not only depend on the latter’s empirical consequences being true but also on them corresponding to the most salient phenomena in its domain of application. In model-theoretic terms: a theory’s empirical adequacy does not only require that (in at least one of its models) all its empirical substructures are isomorphic to the corresponding phenomena [van Fraassen 1976], but also that they are so to all salient phenomena in the domain. The challenge, then, is to characterize the kind of information that, even if logically disconnected from what a theory entails, nonetheless provides crucial evidence for the theory and falls inside its domain of application. From the examples chosen by Laudan, it seems that he has in mind cases in which some striking empirical regularities remain theoretically unexplained, even though they clearly fall within the theory’s domain. As we will see in section 4, the threefold evaluation of theories put forward by Kuipers involves the consideration of what he calls “neutral results” [Kuipers 2005], which amount to Laudan’s non-refuting anomalies and represent an important parameter in the comparative assessment of theory success.

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16 B) Let us now turn to the issue concerning the priority of prediction over accommodation [Lipton 1991, 68], [Forster 2000, 233]. Intuitively, it seems clear that the quality of the evidence provided by predictions is better than that gathered through accommodation. At first glance it appears that this difference in the quality of evidence lays in the way a predictive theory is devised and tested in contrast to how an accommodative theory would be built and evaluated. In the first case, an ad hoc conception of the theory would be more difficult, since the evaluation of the theory would depend on what the theory establishes either about future events or about past events that, even if already known, were not initially targeted by the theory. An accommodative theory, by contrast, could be built just to fit events already included in its initially targeted domain.

17 The above account of the difference between prediction and accommodation, however, is neither completely right nor very enlightening. It is not completely right because it presents accommodation as merging into ad-hoc-ness, when the former does not necessarily imply the latter. The Darwinian theory of evolution, for instance, despite it being more accommodative than predictive, is not regarded as an ad hoc theory. The intuitive account of accommodation is not very enlightening neither, since, regardless of how a theory was initially devised (in an ad hoc, accommodative or predictive manner) it may turn out something different in the future depending on different dynamical aspects concerning theory testing as well as theory evolution. As argued by Peter Lipton, lack of ad-hoc-ness and precision should be emphasized as the most distinctive features of predictions as opposed to accommodations. The implications of ad-hoc-ness will be discussed in the following section. As for precision, one of the main reasons why predictions are precise is that, as opposed to accommodations, they can be subject to experimental control [Lipton 1991, 169]. Anticipating unknown facts, on the other hand, even if clearly constituting an advantage of predictions, does not represent one of its most essential features. Not surprisingly the use of Einstein’s special relativity theory to predict the deviation of Mercury’s perihelion is also mentioned as an instance of a prediction providing stronger support than mere accommodation, despite the fact that such deviation was an already known phenomenon. The soundness of background knowledge and auxiliary assumptions is also mentioned as an indicator of non-ad-hoc-ness.

18 Put in a nutshell, as opposed to what happens with predictive theories, in the case of accommodative theories, the domain of phenomena that prompted the construction of a theory is not different from the domain of phenomena providing the evidential basis to test the theory. This suggests the success condition that the evidential domain of a theory be different from its “construction” domain. This, in turn, would entail a higher independence of the evidence with respect to the theory for which it plays the evidential role, for the evidence involved in testing the theory would not be part of the domain of phenomena that the theory meant to explain.

19 C) Let us turn now to another condition for empirical adequacy such as it is the limited use of ad hoc hypotheses, i.e., non-corroborated auxiliary hypotheses. P. Thagard has established this condition as one of the simplicity criteria for theory choice [Thagard 1978, 86-89], yet in so far as the condition essentially concerns corroboration it can also be understood as a condition to further qualify the empirical adequacy of a theory. According to this author:

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An auxiliary hypothesis is a statement, not part of the original theory, which is assumed in order to help explain one element of F [the facts] or a small fraction of the elements of F. [Thagard 1978, 86, italics in the original]

20 Before this characterization, Thagard has already excluded the possibility that A (i.e., a set of auxiliary hypotheses) be equated with C, that is, a set of un-problematic conditions accepted independently of T or F and assumed in T’s application. Instead, A would include assumptions with narrow applications, restricted in use to one class of fact. As examples, he mentions Huygens’ assumption, in order to explain the irregular refraction in Iceland crystal, that some waves are spheroidal rather than spherical, or his assumption that the speed of light is slower in denser media to explain Snell’s law of refraction. Thagard points out that these assumptions sometimes coincide with ad hoc hypotheses, although he notes that, since ad-hoc-ness is a dynamic property, auxiliary assumptions may lose this ad hoc status at some point. This may occur either because they are at some point confirmed or due to the fact that competing theories share the same assumptions.

21 After severely scrutinizing most common accounts of ad-hoc-ness, both J. Leplin and M. Carrier have separately argued that none of such accounts sufficiently emphasizes the truly distinctive feature of ad hoc hypotheses. Both agree that a hypothesis’ ad hoc character is not determined by the way it was devised but rather by the fact that it does not receive independent empirical support. Both authors converge in pointing to excess empirical content as a key requirement for non-ad-hoc-ness. In Carrier’s terms: A hypothesis explains a fact in a non-ad-hoc manner, if it simultaneously explains at least one additional independent fact that either constitutes an anomaly for the rival theory or that falls beyond its realm of application, i.e., that is neither derivable from nor inconsistent with the competing approach. [Carrier 1988, 206]

22 Although implying some further requirements, J. Leplin’s definition of ad-hoc-ness also includes a condition concerning the lack of independent empirical support [Leplin 1975, 336-337]. Yet, his most novel contribution to the analysis of ad-hoc-ness consists in a condition regarding non-fundamentality. This condition reveals some important aspects related to ad-hoc-ness—like the locally holistic nature of anomalies and the corresponding requirement for hypotheses to solve several anomalies together. The condition, however, also entails some questionable points, specially the presupposition that non-fundamental theories, i.e., those with a wide variety of serious insufficiencies, are the only ones affected by recalcitrant ad-hoc-ness. Given the dynamical nature of theory justification,—which, as recognized by both Leplin and Carrier makes ad-hoc- ness a dynamical, non-stable property—, it may be equally possible that a non- fundamental theory eventually overcomes its difficulties and becomes a fundamental one. Thus, Leplin’s distinction between incomplete theories (where ad hoc hypotheses are eventually changed into non-ad-hoc ones) and non-fundamental theories (where the above possibility is ruled out) does not turn out very helpful to elucidate the question of ad-hoc-ness. On the one hand, we can never be sure that an incomplete theory is not going to end up revealing itself as non-fundamental and, conversely, a non- fundamental one revealing as the opposite. That is the reason why, most often, unanimous judgments about whether a theory is of one kind or the other are made only when a theory has been actually completed or replaced, and yet unanimous judgements about ad-hoc-ness can be made before that happens. Given its questionable character, non-fundamentality is not included here as a necessary condition for ad-hoc-ness. In other words, a general criterion of ad-hoc-ness should enable us to compare two

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theories in terms of their relative ad-hoc-ness regardless of whether we regard either theory incomplete or non-fundamental.

4 Outline of an empirical criterion for theory success

23 The three qualitative requirements for theory success commented above have all something in common: they imply some conditions concerning the relation between a theory and different subsets of its domain. So, before outlining an empirical criterion for theory success that includes the above requirements, several distinctions between different sub-domains of a theory should be drawn. There are two basic divisions: one between successful and unsuccessful intended applications and the other between the construction domain and the evaluative domain. The latter would include four sub- domains: two respectively corresponding to refuting and non-refuting anomalies, on the one hand, and two corresponding to successful predictions and accommodations, on the other. For the sake of simplicity, let us introduce the following notational conventions, all of them referring to domain specifications relative to a theory.

D = domain of application

C = construction domain

E = evaluative domain

ES = successful intended EU = unsuccessful intended

applications applications

EP = successful predictions ER = refuting anomalies

EA = successful accommodations EN = non-refuting anomalies

EAb = ad hoc accommodations.

24 The corresponding sub-domains of a theory are represented in the diagram below. As indicated there, only in the case of ad hoc hypotheses the construction domain and the evaluative domain of the theory completely overlap.

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25 The empirical criterion for theory success can now be outlined as follows:

26 T2 is more empirically successful than T1 if the following conditions hold:

27 1. ES (T1) ⊆ ES (T2),

28 2. EN (T1) ⋂ ES (T2) ‎≠‎∅,

29 3. EA (T1) ⋂ EP (T2) ‎≠‎∅,

30 4. || EAd (T2) || < || EAb (T1)||. 31 Note that these four conditions are here presented as globally sufficient for comparative empirical success, but not as globally necessary, which would reveal as too strong a requirement for most cases of theory choice. As shown in the diagram, in cases of ad hoc accommodations the construction domain and the evalutative domain completely overlap. Non-refuting anomalies of a theory, on the othe hand, are always included within the sub-domain formed by its unsuccessful intended applications.

32 This approach to theory success can be seen as supplementing Kuiper’s complex evaluation matrix by adding some qualitative requirements which are absent from his proposal. In his symmetric models of separate hypothetico-deductive evaluation, i.e., the micro- and the macro-models, for a theory to be at least as successful as the old one, some general conditions of adequacy must be satisfied not only for the definitions of “success” and “problem”, but also for that of “neutral result”—which equates to the notion of non-refuting anomaly. Contrary to what happened in the asymmetric models, where success conditions only refer explicitly to individual problems and general successes while neutral results remain hidden, in the symmetric model the latter play an important role [Kuipers 2005, 52]. By taking all three types of results explicitly into account, Kuiper’s symmetric models meet Laudan’s evaluative requirements concerning the wider scope of most successful theories. Keeping in mind that neutral general facts for a theory constitute neither a problem nor a success, a successful theory should transform general problems into neutral facts (or even successes) and

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neutral general facts into successes. The same kind of requirement should be met at the micro-level for individual successes, individual problems and neutral results. There also neutral instances may remain neutral or become positive.

33 As pointed out earlier, the fine-grained analysis developed by Kuipers fails to incorporate some qualitative parameters—like ad-hoc-ness and accommodation—which prove essential in the evaluation of theory success.

5 Concluding remarks

34 Traditional accounts of theory success have proven in a sense too broad and in another too narrow. The first point becomes evident in the neglect of the problems regarding ad-hoc-ness and accommodation, the second in the insufficient attention paid to issues concerning the application openness or incompleteness of a theory. All these questions, however, seem crucial for a comparative appraisal of theory success. Problems concerning accommodation and ad-hoc-ness would require an analysis of a theory’s level of precision and excess empirical content with regard to its construction domain. Issues regarding narrowness of scope would call for the recognition of non-refuting anomalies as part of the evaluative domain of a theory. The above factors should be taken into account if a theory’s empirical success is to be evaluated in all its complexity.

Acknowledgments

35 I am thankful to Thomas Mormann for helpful comments and references on the subject of theory success. Thanks also to Otávio Bueno for illuminating discussion on the problem of non-refuting anomalies. This work was financially supported by the Spanish Ministry of Economy and Competitiveness through the project Pragmatics as the driving force behind the study of semantic flexibility: conversational contexts and theoretical contexts (FFI2012-33881).

BIBLIOGRAPHY

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KUHN, Thomas S. [1962], The Structure of Scientific Revolutions, Chicago: University of Chicago Press, 2nd edn., 1970.

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KUIPERS, Theo A. F. [2005], The threefold evaluation of theories. A synopsis of From Instrumentalism To Constructive Realism. On Some Relations Between Confirmation, Empirical Progress, And Truth Approximation, in: Confirmation, Empirical Progress, and Truth Approximation, edited by R. Festa, A. Aliseda, & J. Peijnenburg, Amsterdam; New York: Rodopi, Poznan Studies in the Philosophy of the Sciences and the Humanities, vol. 83, 23–85.

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LIPTON, Peter [1991], Inference to the Best Explanation, New York: Routledge, 2004.

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NICKLES, Thomas [1988], Truth or consequences ? Generative versus consequential justification in science, in: PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association, vol. 1988, 393–405.

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NOTES

1. It may be worthwhile to briefly recall Kuhn’s notion of anomaly, since some of Laudan’s points were already suggested by the former, who nevertheless failed to fully realize about their consequences for the traditional conception of evidential support. The general notion of anomaly introduced by Kuhn corresponds to those problems or phenomena that a theory cannot accommodate and that do not fit the theoretical expectations [Kuhn 1962, 58]. Both refuting and non-refuting anomalies fall under the above general notion. Finally, Kuhn, as opposed to Laudan, does not regard it as necessary for an anomaly to be recognized as such that some rival has been able to solve it. On the contrary, he argues that it is the previous awareness of anomaly that initiates the process of theory modification or theory change [Kuhn 1962, 62]. 2. Cf. [Laudan 1977, 29, also n. 15]. Consequently, Laudan equates what has been called “Kuhn’s losses” [Kuhn 1962, 107-108] with certain instances of non-refuting anomalies, namely, those in which the successor theory provides no explanation for phenomena that the previous theory successfully covered. 3. In his 1988 paper, T. Nickles argues that the consequentialist model of scientific justification should be combined with Laudan’s generative model, since the second points to theoretical changes that fall outside the standard conditionalization, which would depend on background knowledge remaining fixed [Nickles 1988, 10]. Although in a different context such as the field of mathematics, I. Lakatos introduced a notion similar to Laudan’s non-refuting anomalies, namely, that of heuristic falsifiers. He explains that, unlike logical falsifiers, which show that a theory as such is false (inconsistent), heuristic falsifiers merely show that a theory does not explain properly what it set out to explain—it is a false theory of the informal domain in question. Therefore, when Lakatos claims that “the crucial role of heuristic refutations is to shift problems to more important ones, to stimulate the development of theoretical frameworks with more content”, the implications that heuristic falsifiers would bear for mathematical theories closely resemble those that Laudan ascribes to non-refuting anomalies in the case of empirical theories [Lakatos 1978, 40].

ABSTRACTS

The purpose of this work is twofold: to explain some of the limitations affecting traditional approaches to theory success, and to outline a criterion for the comparative evaluation of a theory’s empirical success. A special emphasis will be placed on the following issues: a) the superiority of prediction over accommodation, b) the resolution of non-refuting anomalies, and c) the limited use of ad hoc hypotheses. After a first section devoted to the disambiguation of the label ``theory success’’, the second section discusses some major shortcomings of traditional, consequentialist approaches to theory success. Then some clues are provided so as to strengthen the criterion for a theory’s empirical success, which is outlined in the last section.

L’objectif de ce texte est double: expliquer certaines limitations des approches traditionnelles du succès des théories, et esquisser un critère pour l’évaluation comparative des succès empiriques d’une théorie. On insiste sur les points suivants: a) la supériorité de la prédiction sur l’adaptation, b) la résolution des anomalies non-réfutantes et c) l’utilisation limitée d’hypothèses ad hoc. Après une première partie consacrée à lever les ambiguïtés de l’expression « succès d’une

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théorie », la deuxième partie traite de quelques-unes des principales lacunes des approches conséquentialistes traditionnelles du succès des théories. Enfin, dans la dernière section, on esquisse le critère de succès empirique d’une théorie et on donne quelques éléments pour renforcer ce critère.

AUTHOR

MARÍA CAAMAÑO-ALEGRE University of Valladolid (Spain)

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Repositioning Realism

Emma Ruttkamp-Bloem

1 Introduction

1 It is suggested in what follows that realism must be repositioned in order to save it as a viable philosophy of science and thus a new version of realism is outlined. This “naturalised realism” does more justice to current understanding of the functioning of science and its history than either traditional scientific realism or instrumentalism typically does. Naturalised realism is “fallibilist” in the unique sense that it mimics the self-corrective core of scientific knowledge and its progress. This view may sound like a pessimistic meta-inductivist’s dream, but actually this is so only if one views it as a traditional “no-miracles”, “explanationist” kind of scientific realism (compare [Ruttkamp 2011]. Rather the naturalised realist suggests that the current (predominantly explanationist) scientific realist debate should be dissolved into a continuum of possible stances towards the status of theories which are based on the quality of evidence available in support of a theory at a given time.

2 The account of naturalised realism argued for here is unpacked according to four theses: 1) Whether realism or instrumentalism is warranted with regard to a particular theory depends on the kind and quality of evidence available for that theory; 2) Reference is about causal interaction with the world; 3) Most of science happens somewhere in between the extremes represented by instrumentalism and scientific realism on a continuum of stances towards the status of theories; 4) The degree to which realism is warranted has something to do with the degree to which theories successfully refer, rather than with the truth of theories. The conclusion is that realism is alive and well if it can be rescued from the stifling straitjacket of no-miracles imperialism (compare [Mäki 2005]), as Laudan already suggested 3 decades ago [Laudan 1981].

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2 Evaluating science on a continuum

3 The first thesis of the argument for naturalised realism is that whether realism or instrumentalism is warranted with regards to a particular theory depends on the kind and quality of evidence available for that theory. In these terms the realism/ instrumentalism debate is a misguided attempt to take a global attitude towards science, when in fact both of these attitudes are reasonable towards different parts of science at different times in the history of science. The naturalised realist dissolves the extremes of this debate into a continuum of stances towards the status of theories. This “continuum” has been artificially cut up into two discrete positions until now, and these positions then applied to the whole of science. Such “out-of-step-ness” with the history of science is not in line with the arguments for naturalised realism offered here, nor even with more traditional ones such as those offered by Boyd [Boyd 1984], Putnam [Putnam 1984], and others during the past 50 years or so.

4 The point made here is that the real challenge realism faces, rather than focusing on the separate parts/stances making up the continuum, actually has to do with explaining how such a continuum might work as a continuum. The naturalised realist accomplishes this by 1) relating possible stances on the continuum to the type and degree of evidence for theories, and 2) introducing a notion of evolutionary progressiveness. This hangs together with the fallibilist epistemology driving naturalised realism (more on this below).

5 This highlights the second thesis of the naturalised realist argument—namely that reference is about causal interaction with the world (specifically evidence gathering). The naturalised realist construes realism as a particular kind of causal gathering of evidence, and thus stances on the continuum are determined by the number or proportion of purportedly reference-fixing descriptions that fit the current empirical (observational and experimental) data and accompanying theoretical scaffolding. Defining reference as a kind of causal interaction implies realism is appropriate to the extent that there is this kind of interaction.

6 Think of an example from geology—it is currently impossible to reach the solid inner core of the earth which is estimated to be 1,370 km deep, but descriptions of it, based on the behavior of seismic waves, make up explanations of the earth’s structure. However it still seems more plausible to think of the molten core of the earth as really existing, whereas, jumping to physics, it seems to feel more comfortable to simply believe (for now) that quarks are predictively powerful calculating devices and no more. In other words, stances towards the results of causal interaction possible with the core of the earth differ from stances towards the results of interaction possible with quarks. Thus sometimes the “reference” of theoretical terms is so tenuous that the theory incorporating them may be viewed as no more than a device to comprehend the domain being studied to such a degree that it can be explained or predictions can be made about it.

7 On the other hand, reference relations may become more complex and more refined, as scientific theories evolve and progress, and scientific descriptions of and explanations for particular domains of nature multiply and strengthen (e.g., the development of a science such as virology has, at least in terms of some viruses, already run the full gamut of instrumentalism through to realism). In these terms a traditional verdict of instrumentalism can never be final, much rather it is an evaluation of a scientific

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theory that, at that stage, portrays weak reference—or even no reference at all. In its turn, on the other end of the spectrum, realist stances sometimes have to be trimmed back to the barest instrumentalism, e.g., in the case of Newtonian science, where Newtonian descriptions of concepts such as absolute space and time turned out to be misguided, however well-established they had been for centuries. Thus, considered or evaluated over periods of time, science, via its theories, comes to tell entire stories of series of interlaced interactions with aspects of reality oscillating between instrumentalism and traditional scientific realism.

8 These interactions are made up of their own series of to-and-fro movements, which are more than Hacking’s “interventions” in the sense of manipulating unobservables in certain ways, because they incorporate both the empirical and the theoretical aspects of scientific processes [Hacking 1983]. Actually, if one recalls Suppes’ hierarchy of models and theories (and background theories) between the theoretical and experimental level, “interaction” means a constant complex rippling of mutual adapting according to changes at both levels as various parts of networks of theories and models develop through the course of science [Suppes 19 89]. And, if this interaction is taken seriously, then it implies acknowledging that most of science happens somewhere in between the extremes of traditional instrumentalism and traditional scientific realism in continuous to-and-fro movements—this is the third thesis of the naturalised realist argument. Consequently, naturalised realism is not about the triumphant announcement of a single theory’s truth (or success), but rather is about the unfolding of scientific knowledge in series of theories as the result of constant causal interaction between science and reality.

9 An objector to this view might say that even the hardest-nosed realist won’t believe in the approximate truth of very tentative research outputs, while a hardcore constructive empiricist would refuse to believe in unobservables no matter what evidence came in. But this makes the point argued for here—this is indeed how the debate has been cast until now. The account of realism offered here has something to say about the shift from uncertainty to greater certainty (and sometimes to and fro), whereas traditional realists and constructive empiricists typically don’t.

10 This brings us to the fourth thesis: The implication of the no-miracles argument that science and its success can be explained in two ways only, namely via the truth of scientific explanations, or as a miracle, has “rigged” the “game” in a sense and has cost the realist dearly in the sense that realists were forced to give anti-realists much more than was perhaps necessary. Moreover the naturalised realist does not view truth as the property that makes the calls in the realism debate, but rather depicts truth as a pragmatic non-metaphysical notion which is about establishing evidence for realist claims. Truth is a dynamic and functional notion that is constantly made evident or revealed by various relations of reference through the course of investigations of a particular aspect of reality at issue in the history of science.

11 Thus the degree to which realism is warranted in the first instance has something to do with the degree to which theories successfully refer (not with truth as a static notion)— which, in turn, has to do with the nature and extent of our (evidence gathering) interactions with the world. And in these terms truth is assembled—and disassembled and re-assembled—via relations of reference revealing the truth of aspects of reality under investigation bit by bit, always provisionally and through trial and error. And, what precisely it is that can be believed on the grounds of science is evaluated

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continuously at different intervals of the course of science via a causal-descriptivist theory of reference. In these terms “truth” means “warranted assertability” and how “warranted assertability” is interpreted depends on the fallibilist epistemology within which naturalised realism is suggested (see below).

3 Truth as reference1

12 The naturalised realist believes (with classical realists such as Boyd [Boyd 1984], Devitt [Devitt 1991] and others) that science reveals aspects of an independently existing reality to us. In terms of Psillos’ three stances of realism, this is the metaphysical stance of naturalised realism [Psillos 1999]. However, the semantic and epistemic stances are a little bit more complex. The naturalised realist sees the fact that science’s revelations happen piecemeal and tentatively and sometimes at different speeds or in different ways as impacting on the semantic and epistemic stances possible for realists in important ways. To see this first consider some examples of scientific processes: 1) Sometimes the same aspect of reality is investigated from within different paradigms, e.g., many scientists worked on different aspects of cathode rays for different reasons from within different frameworks which led to different “discoveries”, from X-rays, the existence of radium, the phenomenon of radio-activity, Rutherford’s discovery of neutrons and his description of the structure of an atom, through to Bohr’s atomic model, and many others; 2) Sometimes different perspectives that remain different can still be informative—phlogiston vs. oxygen, luminiferous ether vs. electromagnetic fields; 3) Sometimes the same notion is refined through years of investigations of the same aspect of reality and related phenomena—e.g., luminiferous ether in all its guises (e.g., see [Whittaker 1951]). The purpose of these examples is to illustrate that 1) the same aspect of reality can be described in myriad ways through the course of scientific history, and that 2) progress does not necessarily or exclusively imply accumulation, and both of these facts impact on the semantic and epistemic stances of a realist account.

13 More to the point, the goal here is to devise a form of realism that can include, or at least take note of or consider, all descriptions or explanations of a certain real system or phenomenon, rather than just acting from the viewpoint of one of these. Such descriptions include both refinements of previous descriptions and descriptions of the same aspect of reality under investigation from within different (compatible or incompatible) paradigms. Taken very broadly, science consists of a series of processes in which an aspect of reality is studied according to particular theories (and all their “background baggage”) that describe and explain the relevant aspect of reality “adequately” or “successfully” at the time. Then, in time, some theories evolve according to—among other factors not at issue now—changes at the empirical level of science and resultant changes in background theories, which enables them to offer more refined descriptions, conciliations between conflicting evidence, or more detailed explanations of the particular aspect of reality at issue, and so on and so on. Such processes affect a complex network of theories in a specific field of investigation, which are all connected and all impact on each other in the sense that there is growth, revision, change, development, and modification of different degrees at multiple fronts both at the empirical and the theoretical levels of science. This is how truth is assembled and re-assembled. And, the naturalised realist advocates taking (all) these

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kinds of networks into account when the status of theories (i.e., a specific stance on the realist continuum) is considered.

14 Secondly, accumulation is not the only kind of process that guarantees interaction between predecessor and successor theories, since even in cases of “discontinuity” (e.g., phlogiston and oxygen) there is mutual impact. Individual theories that fail to “evolve” or “cannot keep up with” the empirical side of science, shape the networks of theories making up investigation of a certain real system through the course of science, because they point out errors and in that sense “direct” future theory change by indicating necessary adaptations. (This idea is also found in belief revision of the AGM kind, e.g., [Alchourron, Gärdenfors et al. 1985], [Gärdenfors 1990].) In order to do justice to the history of science, surely one must understand why and how scientific theories progress, and not just that they do. To know this depends just as much on the parts of theories that are “adapted” or “rejected” through the course of science than on the parts that are “preserved”. In other words the set of scientific claims representing the “total” knowledge of a real system at a certain time progresses because the available system of knowledge becomes more and more refined as mistakes are corrected and theories are consequently adapted showing that theories that survive are theories that can accommodate revision.

15 And it is this kind of (evolutionary) progressiveness which realism must test and which becomes the criterion for realism as it gives content to assembled truth and the relations of reference revealing assembled truth. Broadly a theory T is “evolutionary

progressive” at time tn iff: 1. it is “empirically (experimentally) adequate” according to experimental practices in the area

of investigation at time tn in such a way that previous versions of theory T at time tn-1 have been adapted in significant ways in order to effect this adequacy, AND

2. it is “theoretically adequate” in the sense that theoretical descriptions made at tn-1 have been adapted such that they describe or refer to observable and unobservable entities in the scope

of the theory at time tn.

16 In this context the different relations of reference underpinning the networks of theories at issue during the course of science offer a mechanism for investigating and fully appreciating the scientific history of interlaced movements relating to the question of more appropriate or adequate levels of adaptation (to instruments, data, anomalies, other theories, etc.)—and thus establishing more appropriate degrees of evidence. The naturalised realist thus views scientific movement not as linear, or converging towards truth, but rather simply as a movement according to current empirical (and theoretical) constraints.

17 As a last step to understanding the semantic and epistemic stances of the account offered here, briefly consider the fallibilist epistemological framework from within which this account of realism is suggested. For current purposes, what is notable is that the problem of realism in science is one of the best ways in which to illustrate a solution to the classic problem of fallibilism—namely how to address the implied paradox in speaking of fallible knowledge and justification in one breath. The solution to the paradox lies in interpreting truth in terms of warranted assertability and acknowledging that beliefs are revisable as long as evidence is revisable. But what can be believed and why? Belief depends on the quality and type of available evidence, nothing more and nothing less. Compare the difference between building a puzzle and building a structure with Lego blocks. There is one way to build the puzzle and the

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outcome is known beforehand. This is not how science works. On the other hand, building a structure with Lego allows for many deviations from the instructions—the same structure can be built with different blocks and the same blocks can be used to build different structures—and one figures all this out as one goes along. This is much closer to how a naturalised realist sees the working of science.

18 Naturalised realism offers an informed way to “thread a course between the rock of fallibilism and the whirlpool of scepticism” [Lewis 1996, 566] because it at least shares Lewis’ [Lewis 1996, 550-551] sentiment that epistemic contextualism must somehow be taken account of when addressing the discomfort one feels in uttering what Rysiew terms concessive knowledge attributions [Rysiew 2001], which are sentences of the form “ ‘S knows that p, but it is possible that q’ (where q entails not-p)” [Dougherty & Rysiew 2009, 123]. In its pure form, epistemic contextualism (e.g., [Schiffer 19 96], [Kornblith 2000], [Stanley 2004], [Schaffer 2004], [Weiner 2005], [Greco 2008], [Rysiew 2011]) implies that belief depends on the “knowledge attributor(s)’ psychology and/or conversational-practical situation” [Rysiew 2001], but for the purposes of the account of realism offered here, this condition is adapted to roughly state that whether or not a statement becomes—or more importantly, remains—a belief depends not on the context within which the statement is made originally so much as on the contexts within which the statement is evaluated through the course of the history of science.

19 Thus, in terms of the epistemic stance of naturalised realism, realism is about truth as warranted belief and thus about the justification of and evidence for beliefs. Realist beliefs are determined by the context from within which philosophers of science evaluate investigations of one aspect of reality over time. This does not mean that realists can never “be in a position to legitimately claim that science has achieved theoretical truth” [Psillos 1999, xx], but it does mean that the content of realist truth claims—and thus what exactly is assembled as “true” at any time—may change according to other changes in the scaffolding of science—which is perfectly in line with epistemic contextualism [Rysiew 2011]. Scepticism is a possibility only if science is depicted in static terms, and naturalised realists consistently emphasise the dynamic fluidity of science. Meaningless relativism is a possibility only if it is not made clear that belief is dependent on evidence which can be rationally articulated and made manifest, which is the naturalised realist’s view. The claim here is precisely that knowledge claims through the history of science must be constantly evaluated and re- evaluated according to newest empirical (and accompanying theoretical) data. This, in turn, implies that what can rationally be believed are knowledge claims whose revision —or perseverance in the face of changed empirical and background situations—can be made sense of throughout the history of science. In other words, the impact of revisions becomes part of how the processes and progress of science are viewed and, in a sense, the fallibility of science’s claims becomes science’s greatest strength because science can state its limits of accuracy which surely makes it infinitely more trustworthy than an enterprise that pretends to have no such limits.

20 Related to this depiction of the epistemic stance, the semantic stance in the naturalised account of realism offered here implies that theories can have truth values, but that these values are never cast in stone. More to the point perhaps, the naturalised realist does not necessarily view semantic claims as existential ones, as she views reference more as an epistemological, than an ontological tool. To see this in more detail, let us consider briefly the account of reference that accompanies naturalised realism. This

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account is based on Stathis Psillos’ causal-descriptivist account of reference [Psillos 1999]. According to Psillos in positing a theoretical entity, some description of fundamental (“kind-constitutive”) properties in virtue of which the posited entity plays the causal role attributed to it is usually offered [Psillos 1999, 294-295]. These properties are described in a “core causal description” associated with the term denoting the posited entity. Specifically, Psillos states that: “1. A term t refers to an entity x if and only if x satisfies the core causal description associated with t” [Psillos 1999, 297]. Furthermore he makes it clear that “...referential continuity requires not a mere overlap in properties, but a substantive continuity in those properties which explain/ground the causal role attributed to the posited entities” [Psillos 1999, 294]. Thus in terms of continuity through theory change, he suggests that: Two terms t and t’ denote the same entity if and only if (a) their putative referents play the same causal role with respect to a network of phenomena; and (b) the core causal description of t’ takes up the kind-constitutive properties of the core causal description associated with t. [Psillos 1999, 294]

21 Psilllos is clear that the core causal description of an entity for which referential continuity is stated must remain preserved when the theory within which it is captured changes [Psillos 1999, 295-297]. He writes: As their causal give-and-take with the world advances, the posited entity is invested with yet more properties which feature in more detailed explanations of the production of its effects. Insofar as these descriptions are mere additions to, and specifications of, the core causal description, there is no change of reference. [Psillos 1999, 295]

22 But, what if these descriptions are not just mere additions? Surely in most cases, at some point in the history of a posited entity, there are also revisions, which may already be implied by “specifications”. Surely descriptions of the fundamental properties of ether must somehow have been revised through all the depictions of the ether from Maxwell’s model, to FitzGerald’s through Thomson’s, to Larmor’s and Lorentz’s portrayal of the ether (e.g., [Whittaker 1951, 292ff.]). If neither the kind- constitutive properties of the causal agent in question, nor the causal role it plays in virtue of these properties, change, to what degree can there really have been theory change and a causal-give-and-take?

23 The naturalised realist suggests, a discussion of referential continuity makes more sense if the emphasis is on the causal role an entity plays in virtue of an empirically adapted core causal description associated with the term denoting the entity. Taking Psillos’ example of “luminiferous ether” referring to “electromagnetic field” [Psillos 1999, 296-298], the naturalised realist broadly agrees that the term “electromagnetic field” plays the same causal role as “luminiferous ether” had been posited to play with regards to light phenomena [Psillos 1999, 296], but she does not state that referential stability is the result of these terms playing the same role in virtue of a basically static (in the sense of absorbing refinements) core of kind-constitutive properties which are the causal origin of both “luminiferous ether” and “electromagnetic field”. Rather she states that it is the result of the respective putative entities—however they are described by current empirical and experimental work—playing the same causal role in virtue of the core set of properties of “luminiferous ether” having been empirically adapted such that they are the properties in virtue of which “electromagnetic field” plays the same causal role as “luminiferous ether” was purported to play.

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24 Specifically, the naturalised realist suggests an account of reference according to which a term t “refers” to a posited entity iff it satisfies a “core causal description” (CCD) of “identifying” properties associated with term t such that 1. the CCD in question has been adapted to fit the current experimental situation and thus describes properties currently thought to belong to the postulated entity and 2. the properties in question are such that the posited entity plays its putative causal role in virtue of these properties (i.e., these properties are the causal origin of claims associated with the putative entity).

25 Note that “identifying” properties are properties that can be described according to the current experimental situation—so “core” properties are properties that have been revised, and are determined by current evidence. Implication: what is “core” can change. What about checking referential stability? This is far less of a frantic issue on this account than traditional insistence on accumulation, because of the fact that realist claims are based on “total” knowledge of an aspect of reality at a given time and thus many more than just one relation of reference is at issue, and moreover the emphasis in terms of “fixing” reference is on revision rather than on exclusively preserving some kind of property. Reference for the naturalised realist is an epistemic issue and is about tracking the development of knowledge concerning a particular target system, phenomenon or event, rather than about establishing the metaphysical existence of a real system, phenomenon or event. In terms of referential continuity of terms through theory change, the naturalised realist thus suggests that terms t and t’ denote “the same” posited entity within the same theoretical system iff 1. both t and t’ each respectively satisfies a CCD of properties associated with them that has been adapted to fit the experimental situations in which the theories containing t and t’ respectively have been formulated, and; 2. the description of the properties in the CCD of t’ has been adapted from the CCD of t, and; 3. the referents of t’ and t play the same causal role with respect to a certain set of phenomena in virtue of the properties described in their respective CCD’s.

26 It is necessary to specify that referential continuity should be considered in terms of “theoretical systems”, as the unit for naturalised realist appraisal is a network of theories, i.e., the collection of all investigations of a particular target system, phenomenon or event over time. And, in this (broader) context, obviously it may the case that not all descriptions of the same posited entity have been adapted from previous descriptions, as there is the real possibility of incompatible descriptions of the same postulated entity—e.g., Thomson, Lorentz, Bohr, Millikan, et al on the properties of electrons—given that the network of investigations being evaluated may include more than one (in/compatible) theoretical system focused on the particular phenomenon or event at issue (e.g., the phlogiston system of theories vs. the oxygen system of theories). (For now, think of a system of theories as broadly a Kuhnian paradigm in the sense of a disciplinary matrix.) Thus the reference relations of every separate theoretical “genre” or system of theories must all be taken into account when a realist decision is made regarding the epistemic stance towards the content of knowledge concerning a particular real system, phenomenon or event at a given time.

27 Acknowledging that descriptions of the relevant properties in the core causal descriptions at issue may differ or change allows for the revision of theories and data typical of the course of science; while the fact that the putative causal entities must play the same causal role in virtue of the respective core causal descriptions associated

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with terms t and t’, allows for referential stability. Note that the two core causal descriptions in the case of t and t’ do not differ in any random manner, rather they differ on descriptions of properties that have been adapted according to new current empirical (and appropriate background) evidence such that 1) it becomes clearer that it is in fact the entity these properties were and are purported to describe which actually plays the causal role it has been said to play, and 2) the core causal description of the putative entity becomes more accurate. Here is thus a true causal give-and-take in the sense that reference, and thus belief in the theoretical constituents at issue, is based on give-and-take between revision and what is preserved.

28 In naturalised realist terms, “referential stability” is actually a kind of methodological continuity. The issue is not so much identifying limiting cases of successor theories or the parts of theories that “persevere” through theory change, but rather the possibility of finding methodological continuity via revisions culminating in evolutionary progressive theories, which, in virtue of their revision, carry on in continuity with their predecessor theories. The naturalised realist account is the only current account of reference that actually deals with the fact that there is interaction between science and world resulting in revision of aspects of theories at issue in science. All other accounts —including Psillos’—focus on preserving somehow some aspect of theories through theory change, and in those terms, establish referential stability. The naturalised realist suggests discussion of the open-endedness of science makes more sense if one turns away from static kind-constitutive properties to ones adapted according to current experimental constraints, because the emphasis in terms of what “endures” in naturalised realism is not on a core description of “central” properties of an entity, but on the causal role an entity plays in virtue of an experimentally adapted core description of properties associated with the term denoting the entity.

29 This account of reference illustrates that both extremes of the realist continuum and, most importantly the positions between them are part of the history of science and must be dealt with by a realist account of science as it allows the full movement from heuristic continuity of terms (e.g., how the demise of phlogiston impacted on the discovery of oxygen) to the (rare) kind of referential stability classical realists would like. In this sense the naturalised realist account implies that those theoretical constituents that in the face of change in type or degree of evidence have been revised to various degrees (or, in the traditional ideal cases, have remained unrevised) can be justifiably believed. The fact that beliefs may have to be rejected at some point, or may become more firmly entrenched, is a matter of history and of the fallibilist nature of human knowledge, nothing more. Moreover as long as “available evidence” is a dynamic notion, revision of belief will be required.

4 Conclusion

30 This account of realism is called “naturalised”, because it mimics the course of science, and continuously establishes or re-evaluates evidence for scientific knowledge via relations of causal reference. In this sense realism is also, just as science, given the chance to state its limits of accuracy while at the same time there is a sense of consensus on the realist content (compare [Gilbert 19 90]) carried by relations of reference establishing a collated view of a given aspect of reality over time. And, the naturalised realist believes it is this kind of action—evaluating, interpreting and re-

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interpreting the processes of science—which is what realism actually should be about, rather than supporting some idealistic view of theories always getting everything “right”.

31 Thus science can be trusted because its theories are challengeable, not because they are invincible (compare [Ruttkamp-Bloem 2013]), and reality is constantly revealed in different guises as a result of science reacting to such challenges. It is concluded that a realism which focuses on science’s ability to self-correct as the result of interacting with reality is preferable to one which focuses on convergence to the “truth” as the result of correct or unique representations. In this way realism can—perhaps for the first time—come into its own as an honest evaluation of science and its history because the focus is on following the trials and errors of science rather than on an empty glorification of science.

BIBLIOGRAPHY

ALCHOURRON, Carlos, GÄRDENFORS, Peter, & MAKINSON, David [1985], On the logic of theory change: Partial meet contraction functions and their associated revision functions, Journal of Symbolic Logic, 50, 510–530.

BOYD, Richard [1984], The current status of scientific realism, in: Scientific Realism, edited by J. Leplin, Berkeley: University of California Press, 41–82.

DEVITT, Michael [1991], Realism and Truth, Princeton: Princeton University Press, 2nd edn.

DOUGHERTY, Trent & RYSIEW, Patrick [2009], Fallibilism, epistemic possibility, and concessive knowledge attributions, Philosophy and Phenomenological Research, 78(1), 123–132, http:// dx.doi.org/10.1111/j.1933-1592.2008.00234.x.

GÄRDENFORS, Peter [1990], The dynamic of belief systems: Foundations vs. coherence theories, Revue Internationale de Philosophie, 172, 24–46.

GILBERT, Alan [1990], Democratic Individuality, Cambridge: Cambridge University Press.

GRECO, John [2008], What’s wrong with contextualism?, The Philosophical Quarterly, 58(232), 416– 436, http://dx.doi.org/10.1111/j.1467-9213.2008.535.x.

HACKING, Ian [1983], Representing and Intervening. Introductory Topics in the Philosophy of Natural Science, Cambridge: Cambridge University Press.

KORNBLITH, Hilary [2000], The contextualist evasion of epistemology, Philosophical Issues, 10(1), 24– 32, http://dx.doi.org/10.1111/j.1758-2237.2000.tb00004.x.

LAUDAN, Larry [1981], A confutation of convergent realism, Philosophy of Science, 48, 19–48.

LEWIS, David [1996], Elusive knowledge, Australasian Journal of Philosophy, 74(4), 549–567, http:// dx.doi.org/10.1080/00048409612347521.

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MÄKI, Uskali [2005], Reglobalizing realism by going local, or (how) should our formulations of scientific realism be informed about the sciences?, Erkenntnis, 63(2), 231–251, http://dx.doi.org/ 10.1007/s10670-005-3227-6.

PSILLOS, Stathis [1999], Scientific Realism. How Science Tracks Truth, Boston: Routledge.

PUTNAM, Hilary [1984], What is realism?, in: Scientific Realism, edited by J. Leplin, Berkeley: University of California Press, 140–153.

RUTTKAMP, Emma [2011], Interactive realism, South African Journal of Philosophy, 30(1), 41–52, http://dx.doi.org/10.4314/sajpem.v30i1.64410.

RUTTKAMP-BLOEM, Emma [2013], Re-enchanting realism in debate with Kyle Stanford, Journal for General Philosophy of Science, 44(1), 201–224, http://dx.doi.org/10.1007/s10838-013-9220-x.

RYSIEW, Patrick [2001], The context-sensitivity of knowledge attributions, Noûs, 35(4), 477–514, http://dx.doi.org/10.1111/0029-4624.00349.

—— [2011], Epistemic contextualism, in: The Stanford Encyclopedia of Philosophy, edited by E.N. Zalta, Winter 2011 edn., URL http://plato.stanford.edu/archives/win2011/entries/ contextualism-epistemology/.

SCHAFFER, Jonathan [2004], From contextualism to contrastivism, Philosophical Studies, 119(1–2), 73–103, http://dx.doi.org/10.1023/B:PHIL.0000029351.56460.8c.

SCHIFFER, Stephen [1996], Contextualist solutions to skepticism, Proceedings of the Aristotelian Society, 96, 317–333.

STANLEY, Jason [2004], On the linguistic basis for contextualism, Philosophical Studies, 119(1–2), 119– 146, http://dx.doi.org/10.1023/B:PHIL.0000029353.14987.34.

SUPPES, Patrick [1989], Studies in the Methodology and Foundations of Science, Selected Papers from 1951 to 1969, vol. Part I, Dordrecht: Reidel.

WEINER, Matthew [2005], Must we know what we say?, Philosophical Review, 114(2), 227–251, http:// dx.doi.org/10.1215/00318108-114-2-227.

WHITTAKER, Edmund T. [1951], History of the Theories of Aether and Electricity, London: Thomas Nelson and Sons, revised edn.

NOTES

1. Some aspects of this section have appeared in [Ruttkamp-Bloem 2013].

ABSTRACTS

“Naturalised realism” is presented as a version of realism which is more compatible with the history of science than convergent or explanationist forms of realism. The account is unpacked according to four theses: 1) Whether realism is warranted with regards to a particular theory depends on the kind and quality of evidence available for that theory; 2) Reference is about

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causal interaction with the world; 3) Most of science happens somewhere in between instrumentalism and scientific realism on a continuum of stances towards the status of theories; 4) The degree to which realism is warranted has something to do with the degree to which theories successfully refer, rather than with the truth of theories.

On présente le « réalisme naturalisé» comme une version du réalisme qui soit plus compatible avec l’histoire des sciences qu’avec les formes explicationnistes ou convergentes de réalisme. On expose son contenu en se référant à quatre thèses : 1) La question de savoir si le réalisme est garanti par rapport à une théorie particulière dépend du type et de la qualité de preuves disponibles pour cette théorie ; 2) La référence est une affaire d’interaction causale avec le monde ; 3) La plus grande partie de la science se situe quelque part entre instrumentalisme et réalisme scientifique, dans un continuum de positions concernant le statut des théories ; 4) Le degré auquel le réalisme est garanti a quelque chose à voir avec le degré auquel les théories réfèrent avec succès, plus qu’avec la vérité des théories.

AUTHOR

EMMA RUTTKAMP-BLOEM Department of Philosophy, University of Pretoria & Centre for Artificial Intelligence Research, Meraka Institute, CSIR (South Africa)

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Philosophy of Chemistry against Standard Scientific Realism and Anti-Realism

Rein Vihalemm

1 Introduction

1 At the 14th Congress of Logic, Methodology and Philosophy of Science, in Nancy, it happened for the first time in the history of the congresses of LMPS that a special session was devoted to the methodological and philosophical issues of chemistry. In earlier times, it used to be taken for granted that chemistry should simply be classified as one of the physical sciences; this had been assumed in the programmes of the LMPS congresses as well. For instance, at the 12th Congress (held in Oviedo, in 2003) there was still reason to mention this outdated view [Vihalemm 2003b], although by that time philosophical analysis of chemistry had advanced at such a pace for a decade already (since the early 1990s) that the existence of philosophy of chemistry as a relatively autonomous discipline could not be doubted any more.

2 In the present paper, I would like to suggest that philosophy of chemistry can be seen as having a central role in the post-Kuhnian philosophy of science in general and, more specifically, in analysing the debate between scientific realism and anti-realism in standard philosophy of science. The post-Kuhnian philosophy of science construes science as a practice rather than a network of statements. I argue that practical realism can avoid the shortcomings of both standard scientific realism and anti-realism. Knowledge cannot be understood as a representation of the world which is independent of practice, and neither can practice be comprehended outside the framework of the real world.1

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2 Practical realism as an alternative to standard scientific realism and anti-realism

3 By standard scientific realism I mean the conception according to which: 1. there is a mind-independent world (reality) of observable and unobservable objects (the metaphysical-ontological aspect), 2. the central notion is truth as correspondence between scientific statements (theories) and reality (the semantic aspect), 3. it is possible to obtain knowledge about the mind-independent reality (the epistemological aspect), 4. truth is an essential aim of scientific inquiry (the methodological aspect).

4 To be an anti-realist in the debate about standard scientific realism means that at least one of these claims is rejected, and this is regarded—by the standard realists—as a rejection of (scientific) realism as such, though it may actually be a more specified understanding of realism instead of anti-realism—in the general sense of the term. Such is practical realism which avoids, as was already said, the shortcomings of both standard scientific realism and anti-realism. Two main types of anti-realism are empiricist-instrumentalist anti-realism and social constructivist anti-realism. The latter—although it rejects the standard scientific realism—is entirely anti-realist only as its marginal outré variant. One must, however, agree with Joseph Rouse that despite the fact that “both the language and substance of ‘social construction’ was fading away”, there is still a need to explore the assumptions that allowed the debates “to be posed in the problematic terms of realism versus social constructivism” [Rouse 2002, 62-63].2

5 Standard scientific realism can be challenged owing to its abstract character, as being too remote from real practice. It is based on the aforementioned metaphysical- ontological presupposition, which raises the problem of the God’s Eye point of view (as it was called by H. Putnam [Putnam 1981, 49]). Although in the case of empiricist- instrumentalist anti-realism, or in the case of social constructivist anti-realism, which both try to avoid metaphysics—and also in the case of Putnam’s internal realism—there is no problem of the God’s Eye, their critique of realism is not acceptable, since they, too, operate in the context of traditional philosophy of science centered on language and logic, and are not founded on actual scientific practices; even if social constructivists “do attend to the material context of laboratory life [...], continuing a long tradition of text bias, they misdescribe the telos of science and technology exclusively in literary terms” [Baird 2004, 7].

6 Both standard scientific realism and empiricist-instrumentalist (or -constructivist) anti-realism—combined with the idea that progress in science means the constant discovering of new facts, and the interconnecting of these facts in some logical manner by creating theories, thereby acquiring more complete and exact knowledge of the world; so to say, approaching the truth, or its “surrogate”, the empirical adequacy, which is waiting “out there”—have lost in popularity in current philosophy of science, although not entirely disappeared. On empiricism we can say the same as on social constructivism: Social constructivism and [standard scientific] realism are neither live options, nor comfortably dead letters. They are vampires, the philosophical undead that still

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haunt our concepts and interpretations of nature, culture and science. [Rouse 2002, 63]

7 The post-Kuhnian philosophy of science, which is practiced under different names (mainly as some kind of qualified realism, such as “critical”, “constructive”, “experimental”, “non-representative”, “referential” or “naturalistic” realism, but which sometimes may be a version of realism directly referring to practice, such as “pragmatic” or “practical realism”), in most cases tends to be practice-based in one sense or another. Therefore, it seems appropriate to speak about practical realist philosophy of science.

8 In my earlier papers (see fn. 1), I have characterised practical realism by five main theses. I shall reiterate these theses here: 1. science does not represent the world “as it really is”, from a God’s Eye position; 2. the fact that the world is not accessible independently of theories—or, to be more precise, independently of paradigms (practices) developed by scientists—does not mean that Putnam’s internal realism [Putnam 1981, chap. 3] or “radical” social constructivism is acceptable; 3. theoretical activity is only one aspect of science; scientific research is a practical activity whose main form is scientific experiment; the latter, in its turn, takes place in the real world itself, being a purposeful, constructive, manipulative, and material interference with nature —interference, which is, in a crucial way, theory-guided; 4. science as practice is also a social-historical activity: among other things, this means that scientific practice includes a normative aspect which, in its turn, implies that the world actually accessible to science is not free of norms either; 5. though neither naïve nor metaphysical, it is certainly realism as it claims that what is “given” in the form of scientific practice is an aspect of the real world.

9 Or, to express this more succinctly, one could say that science as practice is a way of engaging with the world that allows the world to show how it can be identified in some of its possible “versions”. We are not “world makers”. Yet this is not to say that the world consists of self-identifying objects. Objects are identifiable only through practice —and, in principle, they are identifiable in a potentially infinite number of ways. In this sense, they are inexhaustible, having innumerable aspects and relating to the rest of the world in innumerable ways. As to practice, this is a human activity which consists in social-historical, critically purposeful, normative, constructive, material interference through interaction with nature and society, thus producing and reproducing the human world—culture—in nature. Knowledge, the knower, and the world which is known, are all formed in and through practice.

3 Thomas Kuhn as a pioneer of practice-based philosophy of science

10 Philosophy of science still debates Thomas Kuhn’s concept of paradigm [Kuhn 1970a] which is essentially a practice-based conception [Rouse 1987, chap. 2], [Rouse 1998, 2003]; cf. also [Hacking 1983], [Bird 2000]. I have argued that Kuhnian paradigm specified as a practice-based conception can be used as a criterion of science [Vihalemm 2000; 2004].

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11 Alexander Bird has called pre-Kuhnian philosophy of science the “Old Rationalism”; he dubbed post-Kuhnian thinking the “New Paradigm”, to honour Kuhn’s most famous notion [Bird 2000, 3-7]. Kuhn himself spoke of “aprioristic rationalism” (instead of the “Old Rationalism”), meaning that philosophers of science used to proceed from a concept of rationality which had been borrowed from philosophy, not derived from actual science. The New Paradigm is primarily about taking the actual science seriously. It emphasises that science is not merely a logical, verbal and mathematical system; it is created by human agents, scientists, who belong to a wider community of specialists and operate in a specific system, or “world”, with its characteristic mental and material cultures—i.e., they operate in a “paradigm”. So, the New Paradigm basically means—as stressed by Joseph Rouse—that science is construed as a field of practices rather than a network of statements [Rouse 1987, 26], [Rouse 2003, 116].

12 It should be noted, however, that although it seems justified to speak about pre- Kuhnian vs post-Kuhnian history and philosophy of science, and to interpret Kuhn’s account of science in terms of paradigms as a practice-based approach, this does not mean that Kuhn himself elaborated such a viewpoint and is to be clearly associated with it. Among other things, Kuhn “is widely regarded as a social constructionist” [Wray 2010, 311]. One has to agree with Joseph Rouse’s claim that: Thomas Kuhn’s The Structure of Scientific Revolutions has also been perhaps the most misunderstood. In particular, the depth of his criticism of the representationalist epistemology has often been overlooked. Kuhn has most commonly been read by philosophers as someone who ascribes a leading role to theory in science, who emphasises the noncumulative character of theory change, and who denies the possibility of nonneutral criteria for assessing the cognitive worth of such changes. [Rouse 1987, 26]

13 Also, it is well known that Kuhn himself wrote in “Reflections on my critics” [Kuhn

1970b, 231] that he “is tempted to posit the existence of two Thomas Kuhns. Kuhn 1 is

the author of [...] The Structure of Scientific Revolutions [...] Kuhn2 is the author of another book with the same title”. But, on the other hand, Joseph Rouse is right when he says that Kuhn’s ideas should be developed “further in the direction of an account of science as practice than he himself would be happy with” [Rouse 1987, 27]. I agree with Alexander Bird who states that: in important respects Kuhn failed to break entirely with the preceding tradition. From the naturalistic perspective that has developed in “core philosophy” during the last two to three decades, which in due course spread to the philosophy of science, Kuhn’s views are shot through with commitments to the Cartesian and empiricist traditions he saw himself to be rejecting. Furthermore, I argue that it is only partial rejection of positivism and empiricism that explains the radical appearance of the Kuhnian viewpoint—incommensurability, the conception of progress, the rejection of the concepts of truth and verisimilitude and, arguably the world change thesis, are consequences of positivist and empiricist views that Kuhn retained. [Bird 2000, x]

14 So, when we interpret Kuhn as a pioneer of practice-based philosophy of science and regard him as a critic of both standard scientific realism and empiricism (or perhaps even as a supporter of practical realism), it should be borne in mind that, although he laid the foundations of a new mode of thinking, he did not fully transcend the old tradition himself. As said, Kuhn’s ideas should be developed further.

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4 The role of chemistry in elaborating a practical realist philosophy of science

15 Chemistry is an excellent example for analysing science as a special kind of socio- historical, practical activity, and for elaborating a practical realist philosophy of science. In this context, it is worth pointing out that Kuhn’s views evolved in close contact with chemistry and chemists (or chemists turned non-traditional philosophers of science, like James Conant, Leonard Nash, Michael Polanyi). It can be said that in many ways the “New Paradigm” in philosophy of science was founded on chemistry. When Roald Hoffmann asks, in the title of a paper published in Synthese, in 2007, “What might philosophy of science look like if chemists built it?” [Hoffman 2007], one should better admit that in a certain sense chemistry had already greatly influenced the major change—the turn to practice—in the philosophy of science.

16 Somewhat paradoxically, although the discussion on scientific realism has always been a “major issue in the philosophy of science”, and although it is clearly relevant for the science of chemistry as well (to quote, e.g., [Giere 2005, 150]: “A prototype for debates about scientific realism in twentieth century occurred at the end of the nineteenth century with questions about the reality of atoms and molecules”), until the 1990s “it is difficult to find references to chemistry in these debates [Van Brakel 2000, 20]. It is often assumed that chemistry was a typical positivist science as long as chemists used atomic and molecular models as merely fictions and denied any concern with their real existence. Even when they use notions such as molecular orbitals, chemists do not reify them and often claim that they are mere models or instrumental artifacts. [Bensaude-Vincent 2008, 45]

17 Since the early 1990s, however, philosophy of chemistry has been a rapidly developing branch of the philosophy of science, which has paid proper attention to the problem of scientific realism as well.

18 In the latter connection, and, more specifically, when discussing the relevance of philosophy of chemistry to the development of practical realist philosophy of science, which avoids the shortcomings of both standard scientific realism and anti-realism, I would like to refer first of all to some works, where science is analysed as practice (and chemistry is compared with physics), such as the books by Jaap van Brakel [Van Brakel 2000], Davis Baird [Baird 2004], Daniel Rothbart [Rothbart 2007] and, especially, a recent book by Bernadette Bensaude-Vincent & Jonathan Simon [Bensaude-Vincent & Simon 2008], and a collection of articles with the title Stuff: The Nature of Chemical Substances (edited by Klaus Ruthenberg & Jaap van Brakel [Ruthenberg & van Brakel 2008]).

19 Proceeding from the aforementioned seemingly paradoxical point—that although scientific realism, with such central issues as the reality of atoms and molecules, should clearly be relevant to the science of chemistry as well, it had not really been addressed in the chemical context until the 1990s—we can say that this is where the specificity of chemistry, emphasised several times already, becomes evident: chemistry as a science remained outside the scope of philosophy for a long period of time, because the subject of chemistry is particular kinds of matter (i.e., substances, or stuffs) and their transformations, while in philosophy the fundamental ontology of matter has prevailed [Van Brakel 2000, 20, 71]. Joachim Schummer has written about the tensions between

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stuff and form philosophies (in that context) in [Schummer 2008], but also earlier. In van Brakel’s book, we may read the following: Schummer has argued that [...] there has been a subsequent Entstofflichung (“de- stuffing”) of philosophy, giving utter priority to form over substance or “stuff”: Entstofflichung of science (mechanical world picture) and of language [...]; knowledge of substance reduced to that of secondary properties or to Kant’s Ding- an-sich. Schummer suggests that chemistry is governed by an action-related conception of knowledge as distinct from the emphasis on formalisation and mathematisation of physics. This view doesn’t merely emphasise the interactive aspects of the experimental side of science. The empirical praxis of making new things (new “stuffs”) is different from that of making careful measurements or carrying out “crucial” experiments. There is a greater affinity of chemistry to technology or art than to physics. [Van Brakel 2000, 71]

20 This is why chemistry has been regarded as an “impure” science. Bernadette Bensaude- Vincent & Jonathan Simon have published an excellent book with a characteristic title Chemistry — The Impure Science [Bensaude-Vincent & Simon 2008]. The authors refer to the hybrid nature of chemistry, to “its constant mix of science and technology”: [C]hemistry serves as the archetypical techno-science, unable to restrict itself to the high-ground of pure theory, but always engaged in productive practice. When we look back to past philosophers like Denis Diderot or Gaston Bachelard, we can see that the idea that there are two kinds of science—theoretical and practical—is nothing new. [...] Nevertheless, in the course of the last two centuries, the rise of modern physics has promoted pure theory over other forms of science, making it natural to characterize those that rest at the level of practice as impure if not degenerate. [Bensaude-Vincent & Simon 2008, 5]

21 However, they emphasize that it would be wrong to assume that chemistry lacks theories altogether. The authors state: Indeed, we want to place special emphasis on this idea that theory and substance are co-produced by the chemist in the laboratory. [Bensaude-Vincent & Simon 2008, 6], yet they also say, in another passage—referring to Kuhn’s notion of a “paradigm”—that at times “this theory is restricted to a community sharing a common scientific culture, there is no need to make this theory explicit” [Bensaude-Vincent & Simon 2008, 95].

22 Bensaude-Vincent & Simon find that “the characteristic philosophical stance of the chemist in the laboratory” is “operational realism” and that this should be seen “as a basis for rethinking the terms of philosophy of science” [Bensaude-Vincent & Simon 2008, 8]. I find that their approach can actually be regarded as a version of practical realism. On the one hand, the authors clearly criticise standard scientific realism “concerned with the reality behind the phenomena” and assuming “[...] that the aim of science is or at least should be to represent an external, independent reality” [Bensaude-Vincent & Simon 2008, 210]. Yet, on the other hand, what these authors call “operational realism” should not be identified with “instrumentalism”. This latter term used to apply to the anti-realist philosophical position which treats theories as conventional tools, constructs of the human mind “for calculations or classification without making any claims concerning the reality of the theoretical entities they deploy” [Bensaude-Vincent & Simon 2008, 206]. Chemists [...] rarely question the reality of the tools with which they do their chemical work, be they natural or artificial. [Bensaude-Vincent & Simon 2008, 206]

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23 On the basis of chemistry—due to its practical-realistic nature—the drawbacks of not only traditional instrumentalism or empiricism but also those of social constructivism as a version of anti-realism are clearly seen. In chemistry it is obvious that “action comes first, before conceptualization, nomenclature, or theory” [Bensaude-Vincent & Simon 2008, 6]. In chemistry there is so to speak intimate relationship between practical activity and realism [Bensaude-Vincent & Simon 2008, 209]. As it was already said above, actually only the marginal outré variant of social constructivism is entirely antirealist—“a kind of collective idealism” [Rouse 2002, 68]. However, the way social constructivism in general (i.e., not only its outré version) rejects the standard scientific realism (but not realism as such), when claiming that reality, nature or “the facts” are socially constructed, seems also not very clear and therefore is ultimately still often understood as a version of anti-realism. In contrast to the social constructivism, in the practical realist conception of practice it is recognised that there is no such thing as “the social world” (or the “natural world”) except as reified abstractions from the world. The meanings, agency, institutions, or forms of life with which social constructivists would explain how nature becomes manifest to us are themselves senseless apart from those manifestations; they cannot be an independent explanans. [Rouse 2001, 192-193]

24 In practical realist philosophy, the subject—understood not as an abstract individual, but as a real socio-historical being—and its practical activity, recognised as a legitimate part of objective (material) reality, have objective characteristics as well. The subject is incorporated into reality as its specific component, and mind is no longer regarded as its only constituent property: literally, there are no incorporeal subjects. The impact of practice on reality is brought about not from “outside” but from “within” reality. It is the impact of one form of objective reality upon another—the impact of reality “in the form of activity” on reality “in the form of an object”.

25 The traditional model of knowledge acquisition treats subject and object as separate realities in their specific and independent existence, with their independent sets of characteristics. Activity is one subject’s properties and is, therefore, external to any object. Thus, the object is also external to the activity, and independent of it. The practice-based approach implies instead that practical activity has a status more fundamental than the status of individual object-things. An individual thing is identified as an existent object only through specifically defined activities within the context in which these objects appear as specific invariants. This is especially obvious in chemistry: The assumptions underlying chemical practices do not concern things [as some kind of ready-made objects] such as barium sulphide. More precisely, this sort of “thingism” (chosisme) is not typical of chemists. Two major matters of concern more adequately their ontology: i) a concern for relations, and ii) a concern for action. [...] To be sure, chemists deal with individual substances, and pay attention to their molecular structures. However, these things are only of interest to them in so far as they enter into relations with other units. [Bensaude-Vincent 2008, 50]3

26 Today it is also important to add: When it comes to environmental and societal issues, definitions of chemical substances in terms of their molecular structure are not adequate. Rather it is what they do, or could do, to human tissues that is meaningful. For setting the standards of toxicity and correlative responsibility of industrial companies, distinctions between natural stable capacities and dispositions really matter. Chemical substances have to be clearly redefined by their intrinsic properties as well as by

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the dispositions they acquire in specific circumstances, or the affections they cause on human tissues or senses. [Bensaude-Vincent 2008, 52]

5 From chemistry to the theoretical model of science

27 I am happy to say that this view of chemistry as an “impure science”, or a science with dual or hybrid nature—not only in the sense of being between science and technology, but also as lying between “the two venerable scientific traditions of physics and natural history” [Bensaude-Vincent & Simon 2008, 212]—basically coincides with my own treatment of the dual character of chemistry, which I have been developing for quite a while now.

28 However, somewhat differently from Bens aude-Vincent’s & Simon’s view, I have proposed and developed—proceeding from the very same dual character of chemistry— also a conception of “pure science”, i.e., a conception of science in the specific, narrow sense of the term, namely, as an idealised physics-like science. This idealised science I describe by a theoretical model called φ-science, [Vihalemm 2011a,b, 2007, 2005, 2001], [Vihalemm 1999, 85-88]. φ-Science is constructive-hypothetico-deductive by its nature, in contrast to natural history, which is classifying-historico-descriptive.

29 In this connection, I would like to say that what I find especially valuable in Bensaude- Vincent’s & Simon’s philosophical analysis of chemistry is their insistence that chemistry is of importance not only to philosophy of chemistry, but to philosophy of science in general: It should, by now, be clear [...] that the popular image of chemistry as a superficial empirical science obliged to seek its philosophical foundations in other more fundamental science is quite inaccurate, if not philosophically defamatory. Whether this vision of chemistry is the deliberate construction of philosophers of science with a predilection for physics, or just results from the lack of attention paid to chemists’ concepts and methods, it does great disservice to philosophy, depriving it of an interesting practice-based approach. [Bensaude-Vincent & Simon 2008, 209]

30 Due to its dual character, chemistry provides a good example for analysing the difference between physics-like science and natural history. Analysis of chemistry keeps us from simply identifying exact science with physics. Instead, it suggests that we should find out and explain philosophically why physics has obtained the status of the paradigm of science—as natural as this status may seem to be!—, and to reveal the premises and also the limits of this particular type of cognitive practice. I think that in a sense it all comes down to the simple fact that, in the actual historical practice—in the culture of the technological era and of the scientific world picture—physics has (after Galileo and Newton) obtained the aforementioned status of the paradigm of science so securely and, so to speak, naturally, that it blocks any need for critical reflection, for an analysis of why “physics” has become more or less synonymous with “real science”. It should be realised that theories, laws, concepts, etc., are not scientific simply because they are physical. It is obvious, for instance, that being a mathematically formulated physical theory or law is not itself the reason why this physical theory or law has gained the status of an embodiment of scientificity in general. So, the fact that chemistry is not a purely physical science, in the sense of not matching exactly the paradigm of “science proper”, makes its history a very clear example of the introduction of such a paradigm—which has to do with the constructing

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of scientific concepts and theories and with formulating scientific laws (yet bearing in mind that the terms “scientific” and “physical” are not synonyms)—into a field which was originally non-exact science. For instance, Mendeleev’s periodic law, although not a mathematically formulated law of physics, is a real law of nature; it is exact in the same philosophical sense as are the laws of physics [Vihalemm 2003a, 2005], [Vihalemm 2011b, 101-103].

31 Mendeleev’s periodic law has been one of the most characteristic and, at the same time, most puzzling examples in discussions of chemical laws and theories. This law seems to be essentially different in its nature from the exact laws of classical physics, the latter being usually regarded as a paradigm of science by philosophers. One should realise, however, that the periodic system of chemical elements was established by constructing an idealised system of idealised elements. Reference to the theoretical concept of a chemical element is a fundamental idealisation substantiated by experimental chemistry—namely, a definite position in the periodical system based on the periodic law.

32 Comparing chemistry with physics, the philosophy and methodology of science can learn from the actual history of science what are the premises and limits of a science as exact (or ideal) science. Biology is not a good example because in this case, so to speak, the resistance of the material is too strong. Biology is clearly regarded as an altogether different type of cognitive practice, although, traditionally, it is also called “science” (but of its own type).

33 Of course, nowadays—and similarly to chemistry—biology has also, to some degree, become a discipline with a dual nature: molecular biology and genetics, for instance, are using φ-scientific models. Yet life cannot be constructed from scratch, investigation of living systems requires a classifying-historico-descriptive approach. By the way, physics seems to be acquiring a dual character as well, in a certain sense. The emergence of physical theories concerning self-organisation (as developed by Ilya Prigogine and others) indicates that physics itself as φ-science has certain premises, actual aims and limits [Vihalemm 2007a], [Vihalemm 2001, 195-196, 198].

6 In conclusion

34 Chemistry provides an excellent example for developing the conception of practical realism which is against standard scientific realism on the one hand, and against antirealism on the other. In chemistry, it proves to be so to speak natural that knowledge, the knower, and the world which is known, are all formed in and through practice as the legitimate aspects of objective (material) reality.

35 In their book with a characteristic title Chemistry — The Impure Science the authors Bernadette Bensaude-Vincent & Jonathan Simon refer to the hybrid nature of chemistry, to “its constant mix of science and technology” [Bensaude-Vincent & Simon 2008, 5]. The view of chemistry as “impure science”, or a science with dual or hybrid nature, not only in the sense of being between science and technology, but also as lying between “the two venerable scientific traditions of physics and natural history” [Bensaude-Vincent & Simon 2008, 212] largely coincides with this author’s treatment of the dual character of chemistry, and Bensaude-Vincent’s and Simon’s finding that “the characteristic philosophical stance of the chemist in the laboratory” is “operational

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realism” which should be seen “as a basis for rethinking the terms of philosophy of science” [Bensaude-Vincent & Simon 2008, 8], can actually be regarded as a version of practical realism.

36 Philosophical analysis of chemistry is important not only to philosophy of chemistry, but to philosophy of science in general,4 also including developing—proceeding from the dual character of chemistry—a conception of “pure science”, i.e., a conception of science in the specific, narrow sense of the term, namely, as an idealised physics-like science, a theoretical model called φ-science.

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NOTES

1. In this paper, I assume the practical realist conception of philosophy of science I have developed in my previous papers [Vihalemm 2013, 2012, 2011c, 2001], [Vihalemm 2011b, 104-106], [Vihalemm 2005, 180-181]. 2. I am very sympathetic to the position of Rouse which is presented in the chapter 5 of his book [Rouse 1987, 127-165] under the title “Against Realism and Anti-Realism”. 3. The problem of “thinghood” is actually quite central in realism/anti-realism discussions including when it concerns chemistry. One of the frequently used examples has been the discovery of the hormone TRH within biochemistry which has become known through a book by the supposed social constructivist anti-realists, Bruno Latour & Steve Woolgar [Latour & Woolgar 1979]. I have analysed this example referring to [Rouse 1987, chap. 5], [Hacking 1988], [Baird 2004] as an illustration of the practical realist approach to reality “in the form of activity” [Vihalemm 2012, sect. 4]. In this connection it is also interesting to refer to a so to speak negative case in the analysis of “thinghood”—the case of polywater [Van Brakel 2008, 150-154 and other references therein]. 4. See also reviews on the Chemistry — The Impure Science and the authors’ responses to them (“Book Symposium”) under the informative heading: “Ask not what philosophy can do for chemistry, but what chemistry can do for philosophy” (changetal10).

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ABSTRACTS

In this paper, it is suggested that philosophy of chemistry can be seen as having quite a central role in the post-Kuhnian philosophy of science in general, and in analysing the scientificc realism vs anti-realism debate in standard philosophy of science, in particular. The post-Kuhnian philosophy of science construes science as a practice rather than a network of statements. It is argued that practical realism can avoid the shortcomings of both standard scientific realism and anti-realism. An important recent book, B. Bensaude-Vincent’s & J. Simon’s Chemistry — The Impure Science [Bensaude-Vincent & Simon 2008] is analysed, and the position of the authors is interpreted as a kind of practical realism.

Dans cet article, on suggère qu’un rôle central peut être assigné à la philosophie de la chimie dans la philosophie des sciences post-kuhnienne en général, et dans l’analyse du débat opposant le réalisme scientifique à l’anti-réalisme dans la philosophie des sciences standard. La philosophie des sciences construit la science comme une pratique plus que comme un réseau d’assertions. On soutient que le réalisme pratique permet d’éviter les défauts à la fois du réalisme scientifique standard et de l’anti-réalisme. On analyse un livre important publié récemment, B. Bensaude-Vincent’s & J. Simon’s Chemistry — The Impure Science [Bensaude-Vincent & Simon 2008], et on interprète la position des auteurs comme une sorte de réalisme pratique.

AUTHOR

REIN VIHALEMM Institute of Philosophy and Semiotics, University of Tartu (Estonia)

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On the Ontology of Linguistic Frameworks Toward a Comprehensive Version of Empiricism

Majid Davoody Beni

Homer Simpson: I want Chocolate Star Wars. Squeaky Voiced Teen: I am sorry sir. The computer says that the movie Chocolate Star Wars does not exist! Homer Simpson: I say you don’t exist!

1 Introduction

1 “Do unreal objects exist”? After the publication of Bertrand Russell’s brilliant “On Denoting” [Russell, 1904], it became too incautious to give a sure positive answer to the question. Perhaps it was Russell’s gifted manners in putting arguments in their precise logical forms, or his wits in spoofing away anything contrary to his cultivated philosophical taste, or simply his reputation as the heir of the British empiricists, which persuaded the fellow-empiricists like Schlick [Schlick, 1915] and Quine, [Quine, 1951, 1947] to dismiss the Meinongian answer to this question as irrelevant and misleading. Thus Meinong was destined to be the empiricists’ public enemy No. 2, next to no one else but Plato himself. Surprisingly enough, even the traditional Meinongians read him in this extraterrestrial platonic light (for example see [Castañeda, 1974], [Routley, 1980], [Lambert, 1983]). Recently, however, it has been shown that Meinong deserves to be defended in surer and more naturalistic setting, see [Davoody Beni, 2013]. I will go one step further than that: the bitter enemy (i.e., Meinong) turns out to be a sweet friend, and far from endangering the main tenets of empiricism, his accomplishments may be used in the way of fixing some shortcomings of the Carnapian philosophy.

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2 Historically speaking, Carnap was the heir to Russell who was the principal heir to pure- blood old British empiricists in his turn. For empiricists “to account for the external world as a logical construct of sense-data—such, in Russell’s terms, was the program. It was Carnap, in his Der logische Aufbau der Welt of 1928, who came nearest to executing it” [Quine, 1951, 74]. Quine’s account of Carnap’s program has been somewhat challenged in the recent literature, see [Friedman, 1987], [Richardson, 1990]. But this does not need to be a source of concern in our enquiry. Neo-Kantian influences on his thought granted, Carnap could still be assumed to be under Russell’s spell in some salient aspects.1 Ironically, while Carnap’s ancestor (Russell) and Carnap’s descendant (i.e., Quine), both were the headstrong critics of Meinong’s philosophy and its ontological consequences, the Meinongian view would be appealed to in fixation of Carnapian empiricism, at least to the extent that the problem of abstract entities is at issue.

3 Technically speaking, Carnap was deeply concerned with the philosophical questions about designation of the terms allegedly referring to abstract entities. In spite of his concern, Carnap did not endorse any ontological approach to the question, and tried to deal with them in purely semantical terms. And this is exactly the point where Carnap’s thought clashes to Meinong’s. Meinong devised an ontological system which included all kinds of everything, existent, subsistent, or even extra-existent, all together in one system.

4 Notwithstanding the traditional understanding of the relationship between the empiricist camp and Meinong, in this paper I suggest that far from contradicting the empiricist agenda, and in a compromising move, the Meinongian view supplies the Carnapian program, and promotes it in the way of coming to a final solution for the problem of existence of abstract entities, and, finally in the way of accomplishing a comprehensive version of empiricism.

2 The empiricist’s dilemma

5 The story of how Carnap’s semantical approach evolved out of his syntactical endeavor, the role of Tarski in this evolution, and its gains and losses are discussed by Carnap and others on different occasions (for example see [Carnap, 1963, 30] and [Creath, 1998, 1990, 61]). We do not need to focus on the historical context here. What is more important, for us, is to mull over some significant gains that Carnap has earned out of the semantical approach.

6 On an ordinary reading, semantics is supposed to be concerned with the referential relation between the terms of a language on one hand, and the referents dwelling in an extra-linguistic sphere on the other hand. In this sense, adopting a semantical approach may commit us to the existence of the external world or a platonic heaven which includes the referents of the abstract entities.

7 But Carnap took a different route. He defined a semantical system as a “system of rules, formulated in a metalanguage and referring to an object language, of such a kind that the rules determine a truth-condition for every sentence of the object language, i.e., a sufficient and necessary condition for its truth” [Carnap, 1942, 22]. Carnap’s view was obviously influenced by Tarski’s austere, and even deflationary, approach. According to Tarski,

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[...] the semantic definition of truth implies nothing regarding the conditions under which a sentence like [...] snow is white can be asserted [...]. Thus, we may accept the semantical conception of truth without giving up any epistemological attitude we may ever have had; we may remain naive realists, critical realists or idealists, empiricists or meta-physicians-whatever we were before. The semantic conception is completely neutral toward all these issues. [Tarski, 1944, 362]

8 Empiricists’ unwillingness for acceptance of ontological commitments was well-known, and if Tarski could dodge the commitment so effortlessly, why should Carnap embrace it?

9 It is in this context that in “Empiricism, Semantic, and Ontology” [Carnap, 1950, hereafter ESO], Carnap addressed the problem of existence of abstract objects by drafting what I call the empiricist’s dilemma; the dilemma posits the views of the majority of empiricists, who generally felt themselves in “much more sympathy with nominalists”, against others who were accused of being Platonists. It holds that: • Regarding the abstract terms,2 either we should call them meaningless (i.e., referent-less) and become nominalists, or we should commit ourselves to Platonism.

10 With respect to any kind of abstract entities, such as properties, classes, relations, numbers, propositions, etc., the empiricists felt much more in sympathy with nominalists than with realists. But for Canap “acceptance of a language referring to abstract entities does not imply embracing a Platonic ontology but is perfectly compatible with empiricism and strictly scientific thinking” [Carnap, 1950, 85, emphasis is mine]. If Carnap could argue for his claim, the dilemma would have been eliminated, and a more comprehensive version of empiricism would have emerged. Let’s go for some further details.

11 Carnap’s principal strategy for dealing with the problem has been based on differentiating between internal and external questions. Internal and external were defined with regard to the borders of the Linguistic Framework (hereafter LF). In this view, internal questions were questions about the existence of certain entities within the framework of an accepted language. The external ones were questions concerning the existence or reality of the system of entities as a whole. Carnap’s groundbreaking solution emerged right there: only the questions of the first kind were considered to be legitimate. The members of the latter group were actually pseudo-questions. Every question, explanation and justification had to be put forward, only after the establishment of the framework. In Carnap’s words: Many philosophers regard a question of this kind [about the existence and reality of entities] as an ontological question which must be raised and answered before the introduction of the new language forms. The latter introduction, they believe, is legitimate only if it can be justified by an ontological insight supplying an affirmative answer to the question of reality. In contrast to this view, we take the position that the introduction of the new ways of speaking does not need any theoretical justification because it does not imply any assertion of reality. [Carnap, 1950, 91]

12 Once the framework has been settled, its pertinent internal questions could be answered either by logical or empirical methods. The concept of reality occurring inside framework was an empirical, scientific, logical and in anyway a non- metaphysical concept.

13 In this way, by a simple waving of the semantical wand, the dilemma has vanished. The moral of Carnap’s paper was that nominalism, as the thesis which denies existence of

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abstract entities, is every bit as metaphysical as Platonism. Carnap’s semantical approach, on the other hand, was devised to be neutral, and even elusive, with regard to the metaphysical questions.

3 Failures

3.1 The inside, the outside, and introduction of new entities

14 Carnap’s semantical approach with regard to the existential questions is pleasantly sophisticated, but it is not consistent with our most common (and perhaps naïve) intuitions about reality. Our intuitions have been known to be misleading previously, and they do not deserve to be trusted blindly. But the inconsistency between Carnap’s approach and the common sense has to be highlighted all the same. Let me elaborate.

15 First of all, as one Archytas of Tarentum pointed out for the first time, it is strange ipso facto, to have some inner space without having the pertinent adjacent outer space. Imagine that we are encircled in a circle suspended in the void, deprived of the existence of any adjoining outer space to encompass it. Now what happens if we stretch a hand (or a spear) outside the circle? Does the spear simply vanish into the thin air? Apparently there lies a problem (or an antinomy, in Kantian terms), even when there are ontological-linguistic spaces that we are talking about. Let me translate the example of the outstretched hand into the Carnapian vocabulary.

16 There certainly was a time when people didn’t speak about electrons, and then speaking about them became current in the scientific circles and everyday talks. Did electrons not exist before that? What is the story of their genesis? Did the physicist say let there be light and electrons began to run all through the wires of creation? We can ask the same question about existence of any other scientific entity in the same tone.

17 I understand that, to the old Archytas’ dismay, Carnap could deal with this objection masterfully: after a significant discovery, the linguistic system changes, the LF would give place to a new one which is more convenient for speaking about the new situation. Introduction of new entities as new variables into the LF does not need any theoretical justification, because they follow from the rules which are laid at the foundation of the framework, see [Carnap, 1950, 89].

18 Therefore, there are some rules of inference and some postulates, laid at the foundation of the linguistic system. These rules are responsible for the emergence of other true sentences of the system. Let us deliberate this axiomatic aspect.

3.2 The role of experience in the constitution of axioms

19 As we saw Carnap’s conception of the linguistic system was an axiomatic one. What does it mean? Does this mean that the sentences of the system are derivable in a deductive manner? If so, what is the role of experience in constitution of the system? Experience should play its role through the choice of axioms, that is, to use Carnap’s terminology, through the choice of the rules of formation and transformation, and in the semantical period, the rules of reference as well. And it does play its role; but in a very complicated and indirect manner. Let me elaborate.

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20 Although in different stages in his work Carnap appealed to descriptive predicates [Carnap, 1932-1937, 30] or F-Truths [Carnap, 1939, 13] to connect his linguistic system to the world of experience, he mostly maintained certain reluctance to go beyond the borders of the artificial language to channel to what lies outside. In other words, as he explicitly remarked in Introduction to Semantics: It is especially important to be aware of the fact that the rules of designation do not make factual assertion as to what are the designata of certain signs. There are no factual assertions in pure semantics. The rules merely lay down conventions in the form of definition of “designation in S”. [Carnap, 1942, 25]

21 But to do justice to Carnap’s thought, I shall remark that he was aware of the peril of hazardous influence of the conventional elements in dislodging his system from the factual world. The choice of linguistic frameworks and their rules are conventional, that is true enough, but the conventional elements which are at work in the choice shall not threaten the objectivity of the system and its relation to the world of experience, because there are factual counterparts involved in the choice of LF which counterbalance the conventional aspects and atone for them: The acceptance and the rejection of a (synthetic) sentence always contain a conventional component. That does not mean that the decision—or, in other words, the question of truth and verification—is conventional. For, in addition to the conventional component there is always the non-conventional component—we may call it, the objective one-consisting in the observations which have been made. [Carnap, 1936, 426]

22 He insisted, almost unalterably, on involvement of factual elements inthe choice of linguistic system, until the mid 1960s (for example see [Carnap, 1966, 68]).

23 There are of course Quinean qualms about the possibility of making distinction between the conventional and the factual elements involved in the choice of LFs. Quine had, elaborately, held that language is “a pale gray lore, black with fact and white with convention”, but there are “no substantial reasons for concluding that there are any quite black threads in it, or any white ones” [Carnap, 1963, 125]. I do not know whether we would be convinced by Carnap’s answer to Quine or not (they are mentioned in [Carnap, 1963, 915–922]), but it is not my primary concern right now either. I have, however, some other concerns about adequacy of Carnap’s account of the relation between the factual and the conventional elements. They are to be spelled out in the next section.

3.3 The practical-theoretical gap

24 Let us assume, in the Carnapian manner, that there are factual and non-conventional elements involved in the decisions which lead to the choice of a certain LF. How are these elements to be reconciled with the conventional counterparts of the choice? As early as 1934, Carnap claimed that the factuality penetrates into the linguistic system through the methodological practical considerations that are at work in the decisions about the choice of LF: The construction of the physical system is not effected in accordance with fixed rules, but by means of conventions. These conventions [...] are, however, not arbitrary. The choice of them is influenced, in the first place, by certain practical methodological considerations (for instance, whether they make for simplicity, expedience, and fruitfulness in certain tasks). This is the case for all conventions, including, for example, definitions. [Carnap, 1932-1937, 320, emphasis is mine]

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25 There are practical considerations however, and as Carnap emphasized, even in ESO, we cannot discuss the choice in a theoretical language which conveys cognitive content [Carnap, 1950, 87]. And if there is any objectivity and factuality interwoven into the fabric of the decision which leads to the choice of the linguistic system, at least we can be sure that they cannot be expressed via our theoretical language. The methodological practical considerations somehow rise above the borders of LF, as extra-linguistic considerations. Therefore the choice remains, at least at the theoretical and epistemic level, as arbitrary as ever.

26 There exists, however, a typical answer to this question. Carnap did not explicitly formulate this answer, but it has a footing in his works: That the conventions constituting the system of justification are at bottom arbitrary poses no threat whatever to the objectivity of the postulates and their consequences. This was of particular concern to Carnap because he thought that all of logic and mathematics, insofar as the claims thereof can be assessed at all, is to be justified as are postulates and their consequences. Once a system of justification is chosen, i.e., once the various terms of the language are given a definite sense, it is a completely objective matter whether B is a consequence of A. It in no way depends on what any person may happen to imagine, think, believe, or know about these sentences. [Creath, 1992, 148]

27 There is some reservation about Creath’s reading though. The objectivity is confused with rule-following in this answer: people can posit conventions and make themselves observe them without letting (thereafter) their imagination and beliefs interfere with the process, and yet the system and all of its constituents can be at best as objective as the roles that the innocent children assume, zealously enough, in playing murderers and judges, when they represent courtrooms in their school theaters.

28 This shall not make us overlook the sunny side; Carnap affirmed half-heartedly that the choice is not totally uninfluenced by theoretical knowledge: The efficiency, fruitfulness, and simplicity of the use of the thing-language may be among the decisive factors. And the questions concerning these qualities are indeed of a theoretical nature. But these questions cannot be identified with the question of realism. [Carnap, 1950, 87]

29 There is a new riddle then: if practical considerations, like usefulness, fruitfulness, etc., are of theoretical nature, why could they not be used as epistemic justifications for the preference of one linguistic framework over another? Apparently, Carnap held (at least in ESO) that the choice of a linguistic framework does not need any theoretical justification, as he was inclined to show extreme tolerance in this choice. I should make a disclaimer: I do not intend to infringe the principle of tolerance, which has been a relic of the syntactical period [Carnap, 1932-1937, section 17, 51] survived into the ESO. I only want to point out that there is no imminent reason for being so conservative about the expansion of the domain of theoretical discussion, or for takinga cynical attitude toward the possibility of conceiving a vaster linguistic framework which could be the context of discussion of the considerations of fruitfulness, efficiency, etc. Bringing these considerations within the LF would presumably change their practical nature to something (theoretically) more discussable. And this (at least the part that deals with the existence of a vast LF) was very much what Carnap himself held to be the case in the later years of his work: I always presupposed, both in syntax and in semantics, that a fixed interpretation of ML [meta-language], which is shared by all participants, is given. This interpretation is usually not formulated explicitly. [Carnap, 1963, 929]

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4 The Meinongian amendment

30 In this section, I try to amend for the insufficiencies that I enumerated in the previous sections. I try to draw, with a few strokes, a rough sketch of an empiricist-friendly system based on the Carnapian foundations.

31 Let’s suppose that there exists a linguistic framework. The Inside of the framework includes terms referring to existent things, as Carnap suggested. If we take the framework of scientific discourse as an example, the inside of the framework would be full of terms which denote scientific entities. But the inside of the framework is not disconnected from the outside, nor did it emerge out of thin air miraculously in the first place. There should be a difference between inside and outside after all, and we cannot treat them on an equal footing, if we take Carnap’s theory of LFs seriously enough. Hence my compromising approach:

32 The Outside of the framework is constituted by terms that are tokens of semi-existing things, rather than being an empty void like Carnap suggested. It is a void full of all kinds of everything. To be more precise, in this picture, the framework of full-fledged existent beings is implemented within a vaster framework of semi-existent ones. But the hierarchy of the frameworks does not need to stop here; outside each inner framework there exists a vaster outer framework, whose denizens do not exist as fully as the dwellers of the narrower framework. It even could be imagined that there is an ultimate framework, the vastest framework which literally includes everything, even some contradictory objects which partake in the least possible degree of being.

33 The assumption of existence of such a linguistic level, with entities that have such a meager share in being, might seem a futile assumption, but the appearances notwithstanding, it has its uses. To use a metaphor, we could expect all virtues of a semantical seed-germinator from this ultimately vast linguistic framework. It works in this way: when we want to refine our discourse and elaborate our views about existence of things, we begin from the vastest framework and, within this framework, we talk (negotiate) about the virtues and the vices of any narrower framework which we are going to choose according to whatever criteria that we may happen to have in mind. The rules of formations and transformations, the entities that are supposed to be embedded within the chosen framework, and any other feature that we want to assign to the framework, all are stored within this seed-germinator. Their existential status is still undecided, and actually tends to zero. Their existential status would be improved, according to the level of a narrower LF in which they would be encompassed.

34 As we remember, for Carnap, in the ontological and metaphysical discourses, it was making commitments to the existence of objects outside any linguistic framework which was repelling. Here, the ontological questions that ask “what entities (or sets of rules) are to be chosen” is constrained within the borders of a LF, though it is an extremely vast LF that we are talking about. Carnap’s reservation about making questions about what lies outside the LF has no bearing on the present situation.

35 Thus, to amend for the narrow-mindedness, which was the weak point of the standard reading of Carnap’s approach, I introduced a vast all-comprehensive framework which could play the role of a seed-germinator for breeding (i.e., discussing) the rules and axioms, and finally the terms-entities, of the narrower frameworks.

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36 This innovation is obviously inspired by the Meinongian idea of categorization of beings in three existential categories. According to this proposal the amount of existence of entities within each framework can be adjusted by a sieving process (i.e., some assessments and evaluations) which take place in a vaster framework.

37 We need not be afraid of the chaotic characteristic of Meinongian ontology in this reading, because the linguistic frameworks may as well work as hedges, in the way of imposing some order to the Meinongian jungle, which has been called by the anti- Meinongian “the breeding ground for disorderly elements” [Quine, 1951, 4]. In this way, we can rest assured that the most significant semantical feature of Carnap’s approach (i.e., the notion of linguistic framework) is retained in this synthesis. Thus, we assume that we are facing different degrees of beings assigned to different classes of entities encompassed within different linguistic frameworks. These are linguistic entities, however, and not the metaphysical objects, which are contained in these frameworks, because according to the Carnapian approach (which is the other counterpart of the synthesis) reality and existence are to be defined only within the linguistic frameworks. So the only adjustment (to the Meinongian system) occurred when I bonded the Meinongian beings within the linguistic frameworks. They do not exist or subsist or extra-exist in a metaphysical world or a Platonic heaven. They are bounded within linguistic regions.

38 The final remark is that the Carnapian conventional elements somewhat persist in this refined picture. Even here, the sentences which are bounded within the framework are not connected directly to the facts, but their truths are determined within a vaster linguistic framework. The designata of the terms of the adopted language are still linguistic entities, to Carnap’s delight. But the important point is that the designation relation is not, even epistemically or theoretically, arbitrary any more. The designation relations are to be discussed and fixed within a wider domain of the underlying framework, which works as the semantical seed-germinator. These discussions take place within the borders of a linguistic framework, and could be considered as valid theoretical discussions. And by the same token, the relation between the abstract entities and their designata would be more robustly established than what a nominalist is willing to accept.

Acknowledgements

39 I would like to thank Richard Creath, Anjan Chakravartty and Mehdi Nasrin for their great remarks and contributions to earlier drafts of this paper. I have also benefited from the comments of the audience participating in the presentation of the original version of this paper, at CLMPS 2011 in Nancy. The organizers helped a lot in preparing my participation in the conference. All of these contributions are gratefully acknowledged.

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BIBLIOGRAPHY

CARNAP, Rudolf [1928], Der logische Aufbau der Welt, Leipzig: Felix Meiner Verlag, English translation by R. A. George, 1967. The Logical Structure of the World. Pseudoproblems in Philosophy. University of California Press.

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—— [1936], Testability and meaning, Philosophy of Science, 3, 419–471.

—— [1939], Foundations of logic and mathematics, in: International Encyclopaedia of Unified Science, Chicago: University of Chicago Press, vol. 1.

—— [1942], Introduction to Semantics, Cambridge, MA: Harvard University Press.

—— [1950], Empiricism, semantics, and ontology, Revue Internationale de Philosophie, 4, 20–40, reprinted in Philosophy of Science, edited by Boyd, R., Gasper, P., and Trout, J. D., Cambridge, MA: MIT Press, 1991.

—— [1963], Intellectual autobiography, in: The Philosophy of Rudolf Carnap, edited by P. A. Schilpp, La Salle: Open Court, The library of living philosophers, vol. 11, 1–84.

—— [1966], Philosophical Foundations of Physics: An Introduction to the Philosophy of Science, New York: Basic Books.

CASTAÑEDA, Hector-Neri [1974], Thinking and the structure of the world, Philosophia, 4(1), 3–40, http://dx.doi.org/:10.1007/BF02381514.

CREATH, Richard [1990], Introduction, in: Dear Carnap, dear Van : the Quine-Carnap correspondence and related work, Berkeley; Los Angeles: University of California Press, 1–43.

—— [1992], Carnap’s conventionalism, Synthese, 93(1–2), 141–165, http://dx.doi.org/10.1007/ BF00869424.

—— [1998], Carnap’s move to semantics: Gains and losses, Alfred Tarski and the Vienna Circle, Vienna Circle Institute Yearbook, 6, 65–76.

DAVOODY BENI, Majid [2013], On what is not there. Quine, Meinong, and the indispensability argument, Humana.Mente Journal of Philosophical Studies, 25, 77–94.

FRIEDMAN, Michael [1987], Carnap’s Aufbau reconsidered, Noûs, 21(4), 521–545.

LAMBERT, Karel [1983], Meinong and the Principle of Independence: Its Place in Meinong’s Theory of Objects and Its Significance in Contemporary Philosophical Logic, Cambridge: Cambridge University Press.

QUINE, Willard Van Orman [1947], Steps toward a constructive nominalism, Journal of Symbolic Logic, 12, 97–122.

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RICHARDSON, Alan [1990], How not to Russell Carnap’s Aufbau, in: PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association, Chicago: The University of Chicago Press, vol. 1: Contributed Papers, 3–14.

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RUSSELL, Bertrand [1904], On denoting, Mind, XIV(4), 479–493, http://dx.doi.org/10.1093/mind/ XIV.4.479, reprinted in (Russell, 1973, 103–119).

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SCHLICK, Moritz [1915], Die philosophische Bedeutung des Relativitätsprinzips, Zeitschrift für Philosophie und philosophische Kritik, 159, 129–175.

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NOTES

1. Carnap’s own intellectual autobiography (Carnap, 1963, 18, for example), and Aufbau (Carnap, 1928, section 3, 124, 183) seem like other reliable sources for showing he was committed to empiricism. This may very well be consistent with his neo-Kantian motives and concerns about objectivity. 2. I am not sure that “abstract term” is meaningful literally, but I use it here to indicate a term which allegedly refers to an abstract entity.

ABSTRACTS

Can the abstract entities be designated? While the empiricists usually took the positive answer to this question as the first step toward Platonism, in his ``Empiricism, Semantics, and Ontology’’ [Carnap 1950], Carnap tried to make a reconciliation between the language referring to abstract entities on the one hand, and empiricism on the other. In this paper, firstly, I show that the ingenuity of Carnap’s approach notwithstanding, it is prone to criticism from different aspects. But I also show how, even without leaving the empiricist research program, the shortcomings could be amended. Following Carnap’s 1950 outset, and adding some apparently untasteful (Meinongian) ingredients, I will sketch a refined way for dealing with the problem of existence of abstract entities within the framework of the philosophy of empiricism.

Peut-on désigner les entités abstraites ? Alors que les empiristes ont le plus souvent considéré une réponse positive à cette question comme le premier pas vers le platonisme, Carnap a tenté, dans « Empiricism, Semantics, and Ontology» [Carnap 1950], d’opérer une réconciliation entre le langage, d’une part, qui réfère aux entités abstraites, et l’empirisme d’autre part. Dans cet article, je montre tout d’abord que, indépendamment son ingénuité, l’approche de Carnap est sujette à critique sous différents aspects. Mais je montre également comment les défauts pourraient être corrigés, cela même sans abandonner le programme de recherche empiriste. En me référant au projet de départ de Carnap en 1950, et en ajoutant quelques ingrédients d’apparence douteuse (de type meinongien), j’esquisserai une solution plus raffinée pour traiter du problème de l’existence des entités abstraites dans le cadre de la philosophie empiriste.

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AUTHOR

MAJID DAVOODY BENI SPER Amirkabir University of Technology (Iran)

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Quine’s Two Dogmas as a Criticism of Logical Empiricism

Artur Koterski

1 Introduction

1 There have been numerous philosophers who have “effectively” objected to logical empiricism. Popper and Kuhn are perhaps the most famous examples here [Popper 1935], [Kuhn 1962]. Mac Lane [Mac Lane 1938], cf. [Awodey 2008, 231ff.], is a less known, but also very important critic. Quine belongs to the group of the most essential reviewers of logical empiricism, but he significantly differs from thinkers mentioned above.

2 Popper never withdrew his criticism of the Vienna Circle, although his factual and interpretive mistakes were often pointed out. (Nowadays, it is clear that they were so severe that his criticism cannot be treated too seriously.) And Kuhn, when he was writing his Structure, opposed neopositivism not even knowing well what it actually was.1 Although Mac Lane demonstrated a fundamental mistake of the analytical criterion of what is called Language II, neo-positivism is not only Carnap, and Carnap is not only the Logical Syntax of Language. Unlike Popper or Mac Lane, Quine did not resort to the claim that, thanks to him, everybody knows that logical positivism is dead.2 Nevertheless, the reader of “Two Dogmas” would rarely have any doubts about whom this far-reaching criticism was directed at: it was Carnap and neo-positivism.3

3 Quine presented “Two Dogmas” at a conference in Toronto at the end of December 1950, cf. [Creath 1991, 386, fn. 1]. His lecture aroused considerable consternation and an instant reaction: his text was published in the Spring of 1951, and two symposiums dedicated to his provocative views were held soon afterwards. Quine’s arguments provoked multidimensional controversies, which have lasted up to now: as Peter Hylton once observed, after fifty years—and we can add: also after sixty years—it is still debatable, what was actually maintained by Quine, at least in the critical part of “Two Dogmas”.4

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4 For the purposes of this article we adopt the following interpretation. In “Two Dogmas” Quine criticised and rejected one of the fundamental claims of logical positivism (and named it the first dogma) and its alleged justification (the second dogma) in an analysis that can be summarised in the following way: There is no known definition or criterion

of analyticity valid in all domains of sentences (let us mark this thesis as AQ). This interpretation, based on Quine’s explanations given forty years after publication of “Two Dogmas”, cf. [Quine 1991, 271], has rather an austere character, and, therefore, one can hope that it will not raise any major objections.5

5 Adopting less cautious readings of Quine’s work, many philosophers saw “Two Dogmas” as the ultimate nail in the coffin of logical empiricism. Without the correct criterion of analyticity, neo-positivism was not able to explain the origin, necessity and cognitive emptiness of logic and mathematics. Without the backup of verificational theory of meaning it was impossible to overcome metaphysics as syntactical nonsense. It was often concluded in a quite characteristic way: “Quine’s frontal attacks on both primary principles of logical positivism in the early 1950s marked the true end of the movement” [Burge 1992, 6], see also [Burge 2003, 199].6

6 Although the results obtained by Quine can be adequately turned against some views held by some logical empiricists in some moments of their philosophical careers, all those reports about the death of neo-positivism, as will be demonstrated below, also turn out to be greatly exaggerated. The logical empiricists not only did reject the theorems criticised by Quine many years before his article, but they also defended a theory, which was a very close equivalent of “empiricism without the dogmas”, with which Quine wanted to replace logical positivism.

7 For this reason “Two Dogmas”, as well as a considerable share of the discussion generated by it, can be regarded as redundant. Moreover, by attributing verificationism and reductionism to logical positivists,7 Quine volens nolens gave his support to the “received view” interpretation of the Vienna Circle, thereby significantly contributing to falsifying the history of philosophy. If so, then his famous paper was not only redundant, but positively detrimental.

2 Two dogmas in the historical context

8 Besides all the reckless interpretations of AQ there is also a more modest position that if Quine’s thesis is right, then the basic tenets of neo-positivists are refuted. However, it is false too, because its antecedent is true, while the consequent is not.

9 Quine’s main complaint concerns the lack of a criterion of analyticity valid “across the domain of sentences in general”. Yet logical positivists were aware that the analytic/ synthetic (hereafter: A/S) distinction was problematic and that it was necessary to introduce some further modification to the division of judgments established by Kant (the first one, of course, was to remove the synthetic a priori judgments). Already in 1930, i.e., duringhis first visit to Vienna, Tarski tried to convince Carnap that the A/S distinction was vague and not objective. After the conversation with Tarski, Carnap wrote in his diary: 8-11 with Tarski in a Café. [...] concerning tautology, he does not want to agree that it says nothing about the world; he thinks that between tautological and empirical sentences there is merely gradual and subjective difference. Carnap’s diary, 1930-02-22; quoted in [Haller 1992, 5]

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10 Tarski presented a further argumentation during one of his talks at the First Congress for the Unity of Science (Paris 1935). He pointed out there that the division of terms into logical and descriptive was arbitrary, what resulted in the arbitrariness of the A/S distinction. In a letter to Neurath, he described some of the results presented in Paris as follows:

11 In Paris [...] I questioned the absolute nature of the division of terms into logical and descriptive ones and of sentences—into analytic and synthetic; I aimed to show that the division of terms is arbitrary and the division of sentences is to be relativised with respect to the division of terms. During the discussion Carnap regarded my remarks as very profound [...]. Tarski to Neurath, 07.09.1936 [WKS, s. d., quoted with the permission of the Wiener Kreis Stichting, Rijksarchief, Haarlem, Netherlands]; cf. [Tarski 1936, 65], [Neurath 1935, 388]

12 Carnap, who appeared to agree with the views defended by Tarski even before the Paris meeting (see Carnap’s diary quoted below), regarded them as “very profound”. Although he never abandoned his work on a distinction between the analytic and the synthetic, at least from that moment on he fully realised that the distinction could not be of an absolute nature. Does it mean, therefore, that Quine’s criticism was fifteen, or even twenty, years late? Let us try to answer this question, going backwards in time from the conference in Toronto (1950).

13 In September 1944 Tarski wrote a letter to Morton White, who would also question the A/S distinction in the future [White 1950]. The letter included the following passage: I think that I am ready to reject certain logical premises (axioms) of our science in exactly the same circumstances in which I am ready to reject empirical premises (e.g., physical hypotheses); and I do not think I am an exception in this respect. [...] I can imagine that certain new experiences of a very fundamental nature may make us inclined to change just some axioms of logic. And certain new developments in quantum mechanics seem clearly to indicate this possibility. [Tarski 1944, 31-32]

14 Earlier, as we saw, Tarski claimed that the difference between tautological and empirical sentences was merely gradual. Here he talks about revisability of logical axioms what means that in his view if the notion of analyticity is to be retained, it has to be relative. If we relate this letter to the aforementioned talk Tarski had in Paris (i.e., [Tarski 1936]), we get very close to “Two Dogmas”. The main difference lies in the conclusion: for Tarski relativity of analyticity was not a problem for empiricism, cf. [Frost-Arnold 2013, 97]. It does not dispel our doubts as for the belated character of “Two Dogmas” yet. In the early forties, Carnap, Quine, and Tarski met at Harvard, where they held numerous talks and the problem of analyticity was one of the covered topics, cf. [Quine 1960, 67, fn. 7], [Carnap 1963, 35-36, 63-65]; see also [Mancosu 2005, 2010, 395-398], [Frost-Arnold 2013, §5]. It is at least possible that it was those discussions which catalysed the development of Tarski’s views, and therefore, the lack of reference to Tarski in “Two Dogmas” is understandable. Perhaps Tarski’s words “I do not think I am an exception in this respect” refer to Quine and point to the intellectual dependency of Tarski’s standpoint.

15 However, even if Tarski referred to Quine indeed, he had also someone else in mind: Ł ukasiewicz. During the Third Polish Congress of Philosophy (Cracow 1936) Łukasiewicz gave a speech where he talked about the rejection of the (absolute) A/S distinction and the possibility of empirical control over the laws of logic:

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Stoic logic was put forth at the vanguard of formal logic. Therefore, there is a need to revise many philosophical views grown on the ground of Aristotle’s syllogistic. To such views I include, among others, the distinction between analytic and synthetic judgments [...]. I include [there also] this persistently ongoing, and an undoubtedly mistaken view [...] according to which deduction does not broaden our knowledge but only expresses explicitly what we implicitly put as our premises [...]. [Łukasiewicz 1936a, 325-326]

16 The criticism presented by Łukasiewicz primarily concerned the Kantian understanding of the A/S distinction. He found it to be faulty and did not see anything to replace it; therefore, he opted for the rejection of A/S division everywhere with the possible exception of the calculus of names. The second part of his claim seems to imply that since deductions broaden our knowledge, then they should be controlled in essentially the same way as “synthetic sentences” cf. [Łukasiewicz 1929, 27-28], [Łukasiewicz 1936b, 129].

17 We could now, perhaps, agree that the ideas voiced in “Two Dogmas’’’ in fact appeared much earlier, but can Tarski or Łukasiewicz be regarded as logical empiricists?8 And the matter is complicated even further, because at more or less the same time, Quine expressed doubts concerning the possibility of framing the A/S distinction. In the Spring of 1933, he visited Carnap in Prague who wrote in his diary after one of their discussions: Quine, 31.3.33 He says after some reading of my “Syntax” MS: Is there a difference in principle between logical axioms and empirical sentences? He thinks not. Perhaps I seek a distinction just for its utility, but it seems he is right: gradual difference: they are sentences we want to hold fast. [Carnap’s diary, 1933-03-31], quoted in [Quine 1991, 266]9

18 On the one hand, it gives us the proof that Quine was one of the earliest sceptics regarding the possibility of the A/S criterion; on the other one, however, we can see once more that Carnap agreed in principle with Quine’s position. In the context of “Two Dogmas” his generally unknown reaction to Tarski’s and Quine’s remarks seems surprising: shouldn’t they have caused rather a vehement protest of the most important protagonist of analyticity? If this is not the case, then maybe the logical empiricists were, in a way, prepared for such comments?

19 Already in the first edition of Logical Syntax of Language, Carnap included a note which confirms the assumption that the necessity to relativize analyticity had been pointed out much earlier than “Two Dogmas” and that this happened in the neo-positivist circles. In the part of the note where analytic sentences are discussed, Carnap says: [...] (“analytic sentences”). This term, which was used in the first place by Kant, has been more sharply defined by Frege [...]. He calls a sentence analytic when, for its proof, only “the universal logical laws” together with definitions are necessary. Dubislav [...] has pointed out that the concept is a relative one; it must always be referred to a particular system of assumptions and methods of reasoning (primitive sentences and rules of inference), that is to say, in our terminology, to a particular language. [Carnap 1934, §14, italics added]

20 The work of Walter Dubislav that Carnap referred to (On the so-called Analytic and Synthetic Judgments) [Dubislav 1926], was published a quarter of a century before “Two Dogmas”.10 In this booklet Dubislav tried to demonstrate that Kant’s A/S distinction was misleading and that making it work necessitated its relativisation, in the way

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summarised by Carnap in the passage quoted above. And this is how Dubislav concluded his own investigations: A judgment is called “analytic” in relation to a system of assumptions and given types of justification when it is possible to justify this judgment properly, even if it is false, simply in virtue of the relevant system of assumptions with the exclusive use of given types of justification; otherwise, when it cannot be characterized as analytic in relation to the relevant system of assumptions and types of justification, it is called “synthetic” relatively to this system as well as to these types of justification. [Dubislav 1926, 24]

21 The same view was held later by Carl Hempel, another representative of the Berlin Group: And [...] purely formal truth is not absolute, for it depends essentially on the formal specifications which we impose on the language in question. One cannot, therefore, say: “Such and such a proposition is analytic”, but only “It is analytic relative to a language which has such and such syntax”. What are called mathematical and logical truths hold, therefore, only in a system of reference whose specification has the character of a convention. [Hempel 1937, 70-71]

22 Quine certainly did not read either Dubislav’s short book, or Hempel’s article11 but perhaps it is not of a great importance: when Quine already knew Carnap’s reaction to “Two Dogmas”, he upheld in the revised version of this paper (1961) [Quine 1961]. But

Carnap, referring directly to AQ, wrote: In case Quine’s remarks are meant as a demand to be given on definition applicable to all systems, then such a demand is manifestly unreasonable; it is certainly neither fulfilled nor fulfillable for semantic and syntactic concepts, as Quine knows [Carnap 1952, 430], cf. [Martin 1952], [Creath 1991, 364-371].

23 Does this limitation invalidate Quine’s criticism of all particular criteria of analyticity? No, but even if this criticism is correct (in any particular case discussed by Quine), it at most points to the more or less serious technical problems. At this point such criticism ceases to be of interest to us,12especially considering that Quine himself eventually announced the criterion of analyticity.13

24 The second dogma of empiricism was reductionism which, according to Quine, lied at the bottom of verificational theory of meaning. It was, however, repeatedly proven that verificationism and reductionism had been rejected by logical positivists already in the thirties, especially on the left wing of the Vienna Circle, to which the main recipient of Quine’s criticism belonged (see the references in [Koterski 1998, 2.2]).

25 Thus, both claims regarded by Quine as the dogmas of empiricism were openly abandoned by logical empiricists many years prior to the publication of “Two Dogmas”.

3 Empiricism without the dogmas

26 As we saw, Quine had serious doubts about the A/S distinction in the early thirties, but he formulated them only in a few personal remarks. His correspondence with Carnap after Harvard included further, and deeper concerns. However, as he admitted, all of this was far from a comprehensive criticism of analyticity his name is today associated with: I had not thought to look on my strictures over analyticity as the stuff of revolution. It was mere criticism, a negative point of view with no suggestion of a bright replacement. [Quine 1991, 267], see also [Quine 1986-1998, 19]

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27 At that time he did not have the idea of empiricism without the dogmas.14 But some logical empiricists did.15

28 In the second half of the thirties, Neurath’s physicalism began to evolve into a sophisticated conception, the so-called encyclopedism. It was a holistic and naturalised theory of science, strongly contrasting with the older or “dogmatic” types of positivism. This kind of empiricism was a very good equivalent of Quine’s empiricism without the dogmas. Because currently there are quite many valuable works devoted to Neurath’s theory of science, we will not go into the details here, see, e.g., [Uebel 2007]. We do, however, want to point to a theory, which in spite of being well known in scientific philosophy circles, was not linked to encyclopedism although it was closely related to it.

29 In 1934, Edward Poznański and Aleksander Wundheiler, both members of the Lviv- Warsaw School, published a paper on “The Concept of Truth in Physics”.16 Their work was written in Polish, but some neo-positivists were acquainted with its basic content. Rose Rand, born in Poland, who was an informal secretary of the Circle, summarized the article in fifteen pages in German. The analysis of archival sources allows us to determine that Rand’s summary was known at least to Carnap, Neurath, and Hempel.

30 Poznański & Wundheiler consider the possibility of retaining the term “truth” in science.17 The studies of the history of science as well as of scientific practice, they maintain, demands the rejection of the hitherto “absolutist” concept of truth, according to which the truth of a proposition is irrespective of (a) a knowing subject, (b) the truth of other sentences, and (c) currently accepted theories in a given discipline. “Truth”, if it is used in physics (in science), has a significantly different meaning, incompatible with the “absolutist” understanding; Poznański & Wundheiler’s aim was to find this meaning. As a result, they propose replacing the “absolute” truth with an “operational” concept, which was empirically characterised as follows: [...] the operational definition of truth includes a group of actions that lead to determining whether a sentence is true, i.e., a group of verification actions. “A sentence is true”, in operational terms, means as much as “a sentence agrees with the system to which it belongs”, or “a sentence obtained common agreement”.18 [Poznański & Wundheiler 1934, 136-137]

31 Here we are only interested in just one claim: in science all true sentences are true only relatively to a certain system. Arguing in favour of truth thus understood, Poznański & Wundheiler describe science in terms of physicalism,radical fallibilism and anti- foundationalism as well as strongly emphasised holism. All those elements were present in Neurath’s, and later in Quine’s, works. The holistic approach is particularly important, because according to Quine (even if he later thought his approach in “Two Dogmas” to be too radical), holism explained the role and character of mathematics and logic better than conceptions of analyticity proposed by Carnap and others, cf. [Quine 1991, 268, 281].

32 Poznański & Wundheiler defended holism, contrasting it with “pyramidism” illustrated in the following way (Fig. 1):

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33 Scheme I represents a system: it is possible to derive from axioms (A’s) in a more or less direct way all sentences that form this system. However, science is not a system in this sense. It does not resemble a pyramid, but rather a net where all sentences (and their acceptance) are more or less directly interrelated (see Fig. 2).

34 The net in the scheme II has a slightly irregular but still concentric structure with insets at its edge. Therefore, it may also represent Quineian “field of force”: there are knots closer to the centre of the net—a place of logic and mathematics—and those which are not there, i.e., all “synthetic” sentences with the insets on the peripheries which “impinge on experience”. Since there is no absolute truth in science, some changes on the verge of the net may result even in the most profound modifications of

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the interior because in the case of empirical failure in principle the whole net is judged. And thisis the gist of empiricism without the dogmas. The view of Poznański & Wundheiler, deeply inspired by Duhem’s book [Duhem 19 06], is a counterpart of Quine’s later holism.

4 Summary

35 The doubts concerning the A/S distinction appeared in the 1920s and 1930s and although Quine was one of the first sceptics about the A/S distinction, such scepticism appeared also independently (in the Berlin Group and the Lviv-Warsaw School). Regardless of who was first to criticise it, Quine’s article included comprehensive criticism of the existing conceptions of analyticity, the first since Walter Dubislav’s work was published,19 and he started many philosophically valuable, multithreaded discussions, which make “Two Dogmas” a most important work in twentieth-century philosophy. If we decide, however, that the criticism presented by Quine was not a goal in itself, but a tool to argue for a new type of empiricism, then the advantages of his article are questionable. Firstly, the holistic approaches to empiricism were proposed much earlier, and Quine either did not know about them or perhaps ignored them. Secondly, Quine was fundamentally wrong when he ascribed verificationism and reductionism to the logical empiricists in the fifties.20 In this way he supported the received view interpretation of the Vienna Circle’s philosophy of science, with which he considerably contributed to falsifying the history of philosophy of science.

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WHITE, Morton G. [1950], The analytic and the synthetic: An untenable dualism, in: John Dewey: Philosopher of Science and Freedom, edited by S. Hook, New York: The Dial Press, 316–330.

NOTES

1. See his recollections in [Kuhn 2000, 306]. The similarities between Kuhn’s and the neo- positivist conceptions were pointed out already before Kuhn’s death. Cf. [Reisch 1991], [Earman 1993], [Irzik & Grünberg 1995], see also [Bird 2000, 278-280], [Friedman 2003], [Koterski 2010, 42-43], [Uebel 2011]. 2. Cf. [Popper 1974, 69], [Awodey 2008, 234, fn. 14]. As for the convergence of Quine’s and the neo- positivist stances see: [Isaacson 2004].

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3. Thus, Popper wrote: “[...] Quine published a very interesting critique of the Vienna Circle [...] And he referred to the [...] assumption that all statements are either analytical or synthetical as a ‘dogma of empiricism’. Of course, Quine is quite right” [Popper 1995, 14, emphasis added]. 4. Cf. [Hylton 2002, 11], [Hylton 2007, 52], [Creath 2004, 47]; for an example of a classic text, whose authors try to figure out what exactly Quine’s point is, see [Grice & Strawson 1956]. 5. Here I do not take into consideration the claim sketched in “Two Dogmas” that understanding of the distinction questioned by Quine requires empirical (behavioral) criterion of analyticity, although still in the nineties Quine seemed to suggest that it was the core of his criticism, cf. [Quine Bergström et al. 1994, 69, 75-77]. It turned out, however, that it was possible to provide such a criterion, cf. [Creath 2004, §3], also see below, fn. 13, whereas AQ was not undermined. 6. A different point of view is represented by [Poznański 1960, 362, 386ff.]. 7. Since Quine’s criticism simply refers to the hitherto existing empiricism, it is inevitable that every logical empiricist was a dogmatic. See also below, fn. 20. 8. In case of the former such interpretation is acceptable if we understand logical empiricism widely enough, for example, within the boundaries set by Neurath. Łukasiewicz, however, regarded himself as a critic of the Vienna Circle. 9. Quine did not remember the conversation, therefore, naturally, he could not remember Carnap’s reaction, cf. [Quine 1994, 218]. 10. Of course, this does not mean that Carnap knew this book before 1933 (i.e., Quine’s visit in Prague) or 1930 (i.e., Tarski’s visit in Vienna). 11. Neither had he known Duhem’s book, what may be rather surprising. In the second version of “Two Dogmas” (published in [Quine 1961]) there is a reference to La Théorie physique, added—as Quine himself admits—at the request of... Hempel and Frank, cf. [Quine 1991, 269], see also [Quine 1986-1998b, 619]. Quine, having residual knowledge about Neurath’s works, did not refer to him. As he claims, by the time of “Two Dogmas”, Quine had read only two articles from 1931 and 1932, which Carnap gave him still in Prague, cf. [Uebel 1991, 639, fn. 33]. Quine got better acquainted with Neurath’s views in 1983 when they were presented to him by Dirk Koppelberg. Quine was then impressed by how much his own stance agreed with encyclopedism, cf. [Quine 1998, 736]. On the other hand, Tarski and Carnap were originally mentioned in “Two Dogmas” in a footnote, which mainly referred to the Harvard meetings: “[my] debt to other participants of those discussions, particularly Carnap, Church, Goodman, Tarski and White is great and indefinite [...]” [Quine 1951, 20, fn. 1, emphasis added]. However, in the best known version of “Two Dogmas”, which appeared in the second and the third edition of From a Logical Point of View, that footnote is no longer there. A similar passus is placed instead in the “Preface” [Quine 1961, viii]: Quine, for some reason, decided to remove those rather unspecified acknowledgments from “Two Dogmas”, and defended the claim that the criticism of A/S division, cf. [Quine 1985, 150], [Quine 1991, 266-277] or its origins, cf. [Quine 1986-1998, 16] appeared already in [Quine 1936]. Some criticism of this interpretation were presented in [Creath 1987], [Frost-Arnold 2011, 2013, §4.2]; see also [Mancosu 2005, 331], and below, fn. 14. 12. Quine’s dispute with Carnap eventually comes to a dead end. Quine takes into account the concept of relativised analyticity and admits that it is possible to give a definition of “analytic-in-

L0”—but, he says, it would be arbitrary and too narrow. He is not satisfied with Carnap’s explanation that there could not be too much freedom of choice because what is looked for is an explication of the term as used by philosophers, cf. [Grice & Strawson 1956, 142-143], [Putnam 1962, 360]. Quine was not convinced either that the theory of analyticity was possible only on the basis of pure semantics. 13. Admittedly, it does not solve the problem of analyticity in the form identified in the “Introduction” above, but it is behaviouristic. Cf. [Quine 1973, 78-80, §21], [Quine 1991, 270], see also [Quine 1960, 66-67], [Quine 1986-1998a, 94-95].

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14. Cf. above, fn. 11. In May 1942 Quine writes to Woodger describing his Harvard discussions. In this letter there is passage suggesting that according to Quine and Tarski, and contrary to Carnap, the A/S distinction is an “empty phrase”, and, therefore, that logical and mathematical theories require empirical control, similarly to those of physics, cf. [Mancosu 2005, 331], [Mancosu 2010, 395]. Although these are perhaps the most unequivocal of the currently known words issued by Quine at that time, they were still quite far from the radicalism of “Two Dogmas”. 15. Quine: “The title of ‘Two dogmas’, [...] has proved unfortunate in its unintended but very real suggestion that there is no empiricism without the dogmas in question” [Quine 1960, 68, fn. 7, emphasis added]. 16. For more information about Poznański and Wundheiler, see [Uebel & Koterski, forthcoming]. 17. The limitation, which they imposed on themselves, namely, to relate their analyses exclusively to physics, is highly artificial and the authors themselves do not always comply with it. 18. The criticism of the absolutist conception of truth presented by Poznański & Wundheiler was also used by Neurath in the dispute over semantics with Tarski, Kokoszyńska and Carnap. It is worth stressing that their paper was published after Tarski’s seminal work [Tarski 1933]. 19. Dubislav surveyed theories of analyticity of Kant, Nelson, Bolzano, and Frege; Quine’s article has significantly wider scope but in some way it does not go beyond Dubislav’s main conclusion: A/S division is only possible in its relativised version. 20. Richard Creath thinks it is an uncharitable interpretation of Quine’s text and proposes an alternative reading [Creath 1991]. Regardless of which version is closer to Quine’s intentions, “Two Dogmas” was used—and it was possible due to the way in which Quine wrote there about reductionism and verificationism—to force much more uncharitable evaluation of neo- positivism.

ABSTRACTS

“Two Dogmas” was to demonstrate that logical positivism was possible solely due to unjustified assumptions. Quine aimed to point out that the rescuing of empiricism was possible only if another, holistic approach was accepted. However, Quine’s article was anachronistic already at the time of its publication. The aim of this paper is twofold. Firstly, it will sketch Quine’s argument and contrast it with the views held by Carnap and Dubislav. It will be claimed that Quine’s criticism was late by more than fifteen years. Secondly, it is to examine Quine’s postulate of empiricism without the dogmas and compare it briefly with a theory of Poznański and Wundheiler. It will be claimed that Quine postulate was realized already in the 1930s.

Dans les « Deux dogmes», Quine voulait démontrer que le positivisme logique n’était possible qu’en raison d’hypothèses injustifiées. L’intention de Quine était de montrer qu’il n’est possible de sauver l’empirisme que si l’on accepte une autre approche, holistique. Toutefois, l’article de Quine était anachronique dès le moment de sa publication. Le but de cet article est double. Tout d’abord, on esquissera l’argument de Quine et on le confrontera aux positions de Carnap et Dubislav. On montrera que la critique de Quine était en retard d’au moins 15 ans. En deuxième lieu, on examinera le postulat de Quine de l’empirisme sans dogmes et on comparera brièvement

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à la théorie de Poznański et Wundheiler. On soutiendra que ce postulat avait été réalisé déjà dans les années 1930.

AUTHOR

ARTUR KOTERSKI Maria Curie-Sklodowska University (Poland)

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On A.A. Markov’s Attitude towards Brouwer’s Intuitionism

Ioannis M. Vandoulakis

Acknowledgements I would like to express my gratitude to Prof. Boris A. Kushner, who read an early version of this paper and made important comments, as well as Prof. Sergei S. Demidov for the constructive discussions on this theme. Dedicated to Vadim A. Yankov

1 Introduction

1 In 1956, Arend Heyting (1898-1980) published his Intuitionism [Heyting 1956], that could be characterized as the first compendium of the form of mathematics which was inaugurated by Luitzen E.J. Brouwer (1881-1966) in his dissertation of 1907. In order to help the reader, who may not necessarily think intuitionistically, understand the controversies between intuitionistic way of thinking and other standpoints in the foundations of mathematics, Heyting adopted a dialogical form of exposition. Thus, the book is articulated in the form of dispute between the fictional persons “Class”, “Form”, “Int”, “Pragm”, and “Sign”, which represent classical mathematics, formalism, intuitionism, pragmatism and significism, respectively. Nevertheless, it also has the feature of systematic exposition, because it is divided into eight chapters,1 covering the fundamental parts of intuitionistic mathematics.

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Figure 1: Vadim A. Yankov at the Moscow M. V. Lomonosov University on 4th October 1991.

Photo by Ioannis M. Vandoulakis.

2 Nine years after the original English publication, in 1965, the book was translated into Russian and published in Moscow by Mir Publishers that was specialized in translation of scientific literature during the Soviet era. The translator was Vadim A. Yankov (1935- ), one of Andreǐ A. Markov’s (1903-1979)2 pupil. The later served as the editor. Andreǐ A. Markov is known as the founder of the Soviet school of constructive mathematics. On suggestion by Yankov, Markov added in endnotes a new person—“Con”—representing the constructivist, in Markov’s sense. “Con” expresses Markov’s viewpoint, as it was developed until that time and enjoys a privileged status: he has the advantage of ultimate criticism of all aforementioned representatives, without being liable to criticism. However, Markov focuses his criticism predominantly against Brouwer, whom he perceives as his principal antagonist, and essentially ignores the other representatives, except David Hilbert (1862-1943) whose program to “save” the “precious” mathematical results he characterizes as a pointless undertaking (“What to save and why?”).

3 Markov’s criticism is focused on certain principal points that we consider below. A disadvantage of putting Markov’s exposition in the endnotes, that occupy 33 of the 200 pages of the Russian edition, is that Markov cannot provide a systematic exposition of his constructive mathematics, like Heyting’s exposition of intuitionistic mathematics. In compensation, Markov provides essential references to works published in Russian up to that time that clarify his viewpoint on questions discussed in Heyting’s exposition.

4 These endnotes are very important from an historical point of view, because they are the only written document that expresses Markov’s attitude towards Brouwer’s intuitionism. The text shows that Markov was very critical to Brouwer, at that time.

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Research in Markov’s archive by Nikolaǐ N. Nagornyǐ (1928-2007) has shown that at a later time Markov unexpectedly started striving to bring closer his standpoint to Brouwer’s views [Markov & Nagornyǐ, 1984, 14; 2010, xix]. Heyting took into account Markov’s endnotes in the third edition of his book, in 1971. Thus, these endnotes serve also as a starting point of a historical “dialogue” developed between the mathematical schools of Brouwer’s intuitionism and Markov’s constructivism.

5 Accordingly, we focus in this paper on some central questions, on which Markov has explicitly expressed his views. These endnotes succeed in clarifying the principal differences between Markov’s and Brouwer’s viewpoints on the foundations of mathematics. Although many of his comments are mostly technical, his style remains lively expressive and revealing of Markov’s different states of disposition: some comments are critical, or even ironic, others express Markov’s satisfaction or disagreement with Brouwer’s views.

2 Markov’s principal objections against Brouwer’s intuitionism

2.1 Different understanding of constructive objects

6 In the very beginning of chapter 1, Heyting lays stress on the fact that intuitionism is concerned with mental mathematical constructions, which require a different form of logic.

Figure 2: Andre A. Markov at the Computing Center of the Russian Academy of Sciences.

Photo donated by N. M. Nagorny.

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7 Markov agrees that mathematical constructions require a different form of logic. However, he disagrees with the view that the process of construction is extra-linguistic or mental. He understands it as real, like a process executable in a computer. Thus, by constructive objects Markov understands not mentally conceived objects, but concrete objects, like the letters of an alphabet, that is a (finite or infinite) collection of discernible signs.

8 Accordingly, Markov rejects Brouwer’s assumption that certain objects of mathematics and mathematical operations are sufficiently evident, so that manipulation of these objects by such operations cannot lead to inconsistencies—assumption that is grounded on Kant’s concept of intuition (Anschauung)—and bypasses his view of mathematical propositions (formulae, equations, etc.) as mere images (Bilder) of free mathematical creation.

9 Consequently, in Markov’s view, constructive mathematics study constructive processes and constructive objects generated by them; this needs a new form of logic—the constructive (in Markov’s sense) mathematical logic.

2.2 On the concept of potential infinite

10 At the same passage, Markov objects to Heyting’s view that mathematics from the very beginning “deal with the infinite”. Markov claims that the infinite is introduced in mathematics by abstraction (idealization). He distinguishes between the “unclear” (in Markov’s view) abstraction of the actual infinity, which is used to introduce (unintuitable) complete infinite totalities, and the abstraction of potential realizability3 that abstracts away from any practical spatial, temporal or material limitations in our capacity of constructing (concrete or abstract) mathematical objects. This abstraction enables us to conduct reasoning on as lengthy constructive processes and as large constructive objects as required. Thereby, as constructive objects can be considered only those, which are not generated by abstractions more powerful than the abstraction of potential realizability.

11 Markov assumes a philosophical stand about abstractions in the late 1950s: Abstractions are necessary in mathematics; however, they must not be devised for their own sake and lead where there is no return down to “earth”. We should always remember to pass from abstract thinking to practice, as a necessary step of human cognition of objective reality. In case that the possibility of such a passage is turned out to be too doubtful, it is necessary to reconsider the abstractions applied and try to modify them. [Markov 1958, 315–316]

12 Proceeding in line with this thesis, he understands Brouwer’s mental constructions as potentially realizable, since they have (practically) realizable material constructions as archetypes. In this way, Markov actually reinterprets Brouwer’s idea of potential infinite in terms of his own concept of abstraction of potential realizability, in an attempt to “return down to earth”.

2.3 Mathematical existence

13 Heyting’s claim that in the study of mental mathematical constructions “to exist” must be synonymous with “to be constructed” could not pass unnoticed by Markov.

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14 Markov notes that it is not necessary that any definition indicates an object, falling under this definition, because the construction of such an object can be an open problem; thus, we cannot claim that the object exists, unless we solve the problem. This is the case with definition II of natural number in Heyting’s book [Heyting 1956, 2].

15 Hence, Markov identifies mathematical existence with potential realizability of a construction; however, this is not perceived as a process evolving in time (like in Brouwer’s concept of creative subject or Kripke’s scheme). An object exists whenever it can be indicated as a complete finite word (in an alphabet) or it is given by a pair (letter, algorithm) and it is known that the algorithm is applicable to the letter. In case that such a pair cannot be constructed or the applicability of the algorithm cannot be established, this does not mean that the object does not exist. An object does not exist only whenever the impossibility for the object to be constructed is proved (for instance, if the inapplicability of the corresponding algorithm is proved). In this case, the object under consideration does not exist eternally.

2.4 The question of classification of constructive mathematics

16 The question “under which sciences intuitionistic or constructive mathematics should be properly classified?” is examined in relation to the understanding of constructive processes. In Heyting’s view, mathematics studies certain functions of the human mind and therefore it is more akin to philosophy, history and the social sciences [Heyting 1956, 10].

17 Markov objects to this classification on the grounds that the human mind together with its mental constructions are parts of nature. Such mental constructions, as the construction of greater and greater natural numbers, have material archetypes in reality. On the other hand, mental constructions, such as complex algorithms, are initially conceived as mental constructions, but are implemented afterwards as computer programs. Therefore, mental constructions do not fall under social sciences.

18 Markov slightly develops this viewpoint in an unfinished manuscript written during the last months of his life that was posthumously published by N. Nagornyǐ in 1987. In this manuscript, Markov unreservedly classifies constructive mathematics under technological sciences, because [constructive mathematics] investigate and supply instruments, applied in various spheres of human activity. In this respect, it is like engineering. [Markov 1987, 212]

19 Thus, Markov’s view on constructive mathematics is a viewpoint of a specialist primarily interested in applications of mathematics.

2.5 The concept of number

20 In chapter 2, Heyting explains the concept of natural number and clarifies the difference of the intuitionistic concept from other ways of conceiving natural numbers. Markov does not perceive that there is any essential difference of his view with the intuitionistic understanding of natural number. Specifically, for Markov natural numbers are defined as words of the form |, | |, | | |, etc., over the alphabet |. The abstraction of potential realizability does not allow the formation of “infinite” words or the collection of “all” words over a given alphabet taken for completed entity.

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21 However, Markov notes that Heyting’s concept of sequence of rational numbers is unclear and possibly not constructive. He explains that in his view of constructive mathematics, rational numbers are understood as words of a certain type over the alphabet {|, − /} (“ − ” is the sign of minus, / is the sign of fraction). A sequence of rational numbers is a (normal) algorithm that maps every natural number into a rational number.

2.6 On Church thesis

22 In connection with Brouwer’s examples depending on unsolved problems, Markov develops a lengthy critical argument in defense of Church thesis, stated independently by Alonso Church (1903-1995), Emil Leon Post (1897-1954), and Alan Mathison Turing, (1912-1954) in 1936 and expressing the fact that certain refinements of the concept of algorithm (such as, for instance the concepts of recursive function, of λ-definable function, Turing machines, etc.) are adequate explications of the broad intuitive concept of algorithm.

23 In Markov’s constructive mathematics, Church thesis assumes the form of the principle of normalization of algorithms, which states that every verbal algorithm in an alphabet V is equivalent with respect to V to some normal algorithm in V, or, concisely, every verbal algorithm is normalizable. Your examples are very pleasant and subtle. Each of them is based on some problem unsolved at present. You are obviously convinced that as soon as the problem you use would be solved in one or another way (which may comfortably happen), you will immediately invent another example of the same kind, based on another unsolved problem. Let us free ourselves to imagine that some genius mathematician invented a general method (an “algorithm”) that enables us to solve any single mathematical problem, i.e., to give a correct answer—“yes” or “no”—to any mathematical question, requiring such an answer. Then you will not be able to invent none such problem and you would be apparently compelled to agree on everything with Mr. Class [the representative of classical mathematics]. You are possibly afraid of such a tragic perspective. Of course, you are aware that Church proved the undecidability of the decidable problem [Church 1936] and that there has been proved today several modest “massive” mathematical problems. However, all these results are based on the one or the other refinement of the concept of algorithm (“unified general method”), for instance on the concept of recursive function, and the assumption about the adequacy of this refinement, for instance, on Church Thesis asserting that “recursiveness” is equivalent to “calculability”. It is clear that without digging into the concept of algorithm, no proof of impossibility of decidable algorithm may pass through. If you were not willing to accept Church Thesis or some version of it, then you would be compelled to agree that your divergence with Mr. Class depends on the state of our knowledge at the present time. All your anti-classical propositions should be then considered as de facto truths, not as de jure truths. Do you feel comfortable with that? On the other hand, if you accept Church Thesis and modern theory of algorithms, then this would entail a substantial reform of your mathematical outlook and the transition from intuitionism to constructive understanding of mathematics. [Heyting 1956, 163–164]

24 Church Thesis is a point of fundamental divergence between intuitionism and Markov’s constructive mathematics. Heyting considers this thesis in two of his subsequent papers [Heyting 1962, 1969], arguing against its adoption. In view of this criticism,

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Markov is obliged to give explanations about the possible applications of his own principle of normalization of algorithms and indicate explicitly wherever is used in [Markov & Nagornyǐ 1984].

2.7 On the concept of infinitely proceeding sequence

25 In chapter 3, Heyting defines the most important concept in intuitionistic mathematics, that of the spread and the fan theorem is proved. Before the definition of the spread, Heyting introduces the concept of infinitely proceeding sequences, which is not defined by a definite law, but can be an object of ever-creating mental construction.

26 Markov severely attacks against this concept. He considers that the concept of infinitely proceeding sequence is not at all evident and, possibly, even non- constructive. It is not clear why Markov considers that the concept of infinitely proceeding sequence is non-constructive. A possible explanation might be the indeterminacy or eventual impossibility of practical realization of the acts of determination of the successive components of the sequence. This explanation is suggested by the following comment by Markov: I cannot but feel sorry for the man, whom you are ready to force to do so many [acts of] “free choice” or “dice drops”. My understanding of infinitely proceeding sequence is more human, since algorithms can be executed easily by a computer. And what is most important is that my understanding is constructive. Because the concept of algorithm can be standardised, which makes possible the coding of an algorithm and its recording by “letters” in a fixed alphabet. In turn, algorithms themselves can become constructive objects. It is possible to apply other algorithms to them, which is very important in constructive analysis. Your infinitely proceeding sequences are not constructive objects, and I cannot manage them. [Heyting 1956, 166]

27 Thus, Markov suggests a constructive, in his sense, reinterpretation of the concept of infinitely proceeding sequence in terms of normal algorithm4 [Markov 1954b] and rejects infinitely proceeding sequences as non-constructive objects. Thereby, existence of a mathematical object explicitly means for Markov its algorithmic, not mental, construction.

28 Accordingly, Markov reinterprets Heyting’s definition of spread (given in terms of the spread-law and the complementary law), by substituting the concept of law by the concept of (normal) algorithm. As a consequence of Markov’s constructive understanding of spreads, the fan theorem is no longer true. The fan theorem is refuted by a counter-example, on the grounds of several theorems proved by I.D. Zaslavskiǐ [Zaslavskiǐ 1962].

2.8 Not all intuitionistic theorems are true in constructive mathematics and vice versa

29 Markov also attacks certain intuitionistic theorems that are not true in his own constructive mathematics, outlining a rather complicated picture: some intuitionistic theorems are refutable in Markov’s constructive mathematics, whereas there are theorems in Markov’s constructive mathematics that do not hold in intuitionistic mathematics.

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30 Thus, the intuitionistic form of the Heine-Borel theorem holds true, but it is refutable by a counterexample in Markov’s constructive mathematics [Zaslavskiǐ 1962]. The theorem that a bounded function, which is defined almost everywhere is measurable,5 holds true in intuitionistic mathematics, but it is refutable by a counterexample in Markov’s constructive mathematics [Zaslavskiǐ & Ceǐtin 1962].

31 On the other hand, the proposition that every constructive function of a real variable is continuous everywhere in its domain of definition holds true in Markov’s constructive mathematics [Markov 1958], but not in intuitionistic mathematics.

32 Nevertheless, Markov’s notes do not offer an overall comparison between his own version of constructive mathematics and intuitionism. Certain fundamental divergences are not considered here. For instance, the so-called Markov’s principle of constructive selection [Markov 1954a, 1956, 1962], according to which if a constructive process, given by some prescription, is not potentially infinite, then the process terminates. This principle is essential for the proof of certain theorems in Markov’s mathematical analysis. However, it is not acceptable by the intuitionists, because of the ad hoc use of an indirect argument in it and remained controversial and insufficiently evident even among some Markovian constructivists [Kushner 1973, 45].

33 Relatively few notes are devoted to Logic [Heyting 1956, chapter 7], although Markov’s constructive semantics has deep differences from the intuitionistic one. The semantics for Markov’s constructive logic was a later development; it is based on the idea of hierarchy of (formal) languages [Markov 1974a,b,c,d,e,f,g] . Markov does not state either any new argument against the Law of Excluded Middle.

3 On the reception of Brouwer’s ideas in the Soviet Union

34 The reception of the ideas of intuitionism in the Soviet Union was extremely diverse. Soviet philosophers of mathematics, ardent champions of dialectical materialism, for instance, Vladimir Nikolaevich Molodshiǐ (1906-1986), although they were not satisfied with the underlying Platonism of George Cantor’s set-theoretic conception, they were also hostile to the ideas of “effectivists”, i.e., Émile Borel (1871-1956), Henri Lebesgue (1875-1941), René-Louis Baire (1874-1932), which were close to some of Brouwer’s ideas. The ideas of this group of French mathematicians were perceived as “subjective idealism” and variation of Ernst Mach’s (1838-1916) philosophy of science [Molodshiǐ 1938, 53, 78]. The hostility was strengthened by the fact that Nikolai Nikolaevich Luzin (1883-1950), who was viewed as an adherent to the ideas of the French “effectivists” was accused as “active counter-revolutionary” and persecuted [Molodshiǐ 1938, 78–84]; [Demidov & Levshin 1999]. In general, Hilbert’s formalism and Brouwer’s intuitionism were considered as trends of idealistic philosophy [Molodshiǐ 1938]. Even such a notable mathematician, as Aleksandr Jakovlevich Khinchin (1894-1959) does not escape from a subjective exposition of Brouwer’s ideas [Khinchin 1926].

35 A decisive step towards demystification of Brouwer’s intuitionism in the Soviet Union was done by Andreǐ Nikolaevich Kolmogorov (1903-1987) whose early works on intuitionistic logic [Kolmogorov 1925, 1932] contributed to its establishment as a mathematical discipline, rather than a philosophical doctrine. Kolmogorov’s ideas exerted influence on certain historians and philosophers of mathematics, notably Adolf

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Pavlovich Yushkevich (1906-1993) and Sofya Aleksandrovna Yanovskaya (1896-1966). They knew each other from Odessa,6 and cooperated in propagating Hilbert’s and Brouwer’s ideas. In particular, Yushkevich translated in 1934 Herman Weyl’s (1885-1955) book On Philosophy of Mathematics [Weyl 1934] with an introduction by Yanovskaya, that for long remained in the Soviet Union a primary source of information about the Western developments in philosophy of mathematics. Thus, Brouwer’s ideas became initially known to the Soviet scholars through Weyl’s perception of them. Two years later, Yushkevich translated Heyting’s Survey of Research on Foundations of Mathematics [Heyting 1936], with an introduction by Kolmogorov. Moreover, Yanovskaya seems to have been influenced by Kolmogorov’s criticism concerning the applicability of the Law of Excluded Middle [Yanovskaya 1936, 88].

36 Gradually, the anti-Platonic orientation of Brouwer’s philosophy of mathematics started to be attractive to Soviet philosophers, because it was considered compliant with the principles of dialectical materialism. During the time of the thaw, the severe criticism gave its place to efforts of releasing the mathematical content of Brouwer’s intuitionism from his general philosophical viewpoint. In this line, Brouwer’s concept of intuition was studied, particularly by the Soviet philosopher Valentin Ferdinandovich. Asmus (1894-1975) [Asmus 1963], who distinguished the concept of intuition as used in the context of mathematical problems and mathematical creative imagination from intuition as used in philosophical contexts, which is irrelevant to mathematics. During this period, Markov’s constructive mathematics was flourished and perceived as an approach on foundations of mathematics, alternative to intuitionism.

37 Nevertheless, it has never acquired the status of a trend in Soviet philosophy of mathematics. This was partly caused by the fact that the mathematicians of Markov’s school, including Markov himself, abstained from expressing publicly their philosophical views; they preferred to remain on the solid ground of mathematical proving activity. Moreover, the school included repressed and persecuted mathematicians, such as Nikolai M. Nagornyǐ and Vadim A. Yankov, mentioned in this paper. In particular, Vadim Yankov, the translator and initiator of the exposition of Markov’s viewpoint in Heyting’s book, was involved in the dissident movement, arrested in 1982 and sentenced to four years in prison and three years in exile. He was given amnesty and released in January 1987, and rehabilitated in October 30, 1991. Since then he works in the Russian State University for Humanities.

4 Markov in the context of opposition between the Moscow and Saint Petersburg schools

38 Markov’s reaction to intuitionism goes beyond the horizon defined by Kolmogorov’s interpretation of intuitionistic logic in 1932. His interest in foundations of mathematics was shaped not on the grounds of philosophical discussions, which were prevalent in the Moscow school of mathematics, even during the 1930s, in the circles of Ivan Ivanovich Zhegalkin (1869-1947) and A.N. Kolmogorov, but of his research background in applied mathematics and the theory of algorithms, developed during the time he was in Leningrad.

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39 Traditionally, there was a rivalry between the Moscow and the Saint Petersburg Mathematical Schools. The mathematicians of the Moscow school were tolerant to various philosophical conceptions concerning mathematics and mathematical objects; this tendency goes back to D.F. Egorov (1869-1931), N.N. Luzin (1883-1950), P.A. Florensky (1882-1937), and others [Demidov 1993]. On the contrary, the mathematicians of Saint Petersburg school shared values that were primarily of positivist and Western orientation.

40 This discrepancy assumed the form of open conflicts throughout history, especially after Pafnuty L. Chebyshev’s (1821-1894) death. A vivid expression of the opposition between the two schools is the alleged judgment of the Professor of Saint Petersburg Academy Vladimir Andreevich Steklov (1863-1926) on young Luzin’s dissertation Integral and Trigonometric Series. After browsing the work of his Moscow colleague he asked: where the formulas are here? This is not mathematics, but some philosophy! [Demidov 1999, 414]

41 Markov grew out of the intellectual environment of the Leningrad school. All his educational background and early carrier are connected with Leningrad. In 1935 he became a Doctor of Science in Leningrad University; the next year, he was nominated Professor at the same university. Since 1939 he has worked at the Leningrad Branch of the Steklov Mathematical Institute. While he was in Leningrad, his research was focused on general theory of dynamic systems, topology and measure theory; particularly, he studied algorithmic problems of topology, theory of computable invariants of binary relations, cryptography, etc. Since 1946, he has turned to the theory of algorithms and recursive functions that led him to the introduction of the concept of normal algorithm, independently from the foundational debates.

42 Moving to Moscow in 1955, Markov brings with him, the arsenal of his theory of algorithms as well as the traditional positivist dispositions of the intellectual environment of the Leningrad school. By his “algorithmic” approach, Markov tends to “free” intuitionism from its underpinning metaphysical assumptions. It would be rather superficial to interpret this fact as an impact of the governing ideology of dialectical materialism. Markov’s attitude can be better explained as an impact of positivistic disposition and his earlier research on applied mathematics and algorithmic problems, during the period he spent in Leningrad (1933-1955).

43 Thus, his research orientation in Leningrad was shaped under the influence of the mathematical style and values prevailing in the Saint Petersburg Mathematical School, which is characterized by the proclaimed primacy of applications and the search for rigor and effective solutions . This spirit determines also his criticism of Brouwer’s intuitionism and his tendency to “free” it from its underlying philosophical assumptions.

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DEMIDOV, Sergeǐ S. & LEVSHIN, Boris V. [1999], Delo akademika Nikolaya Nikolaevicha Luzina. [The case of Academician Nikolai Nikolaevich Luzin], Saint Petersburg: Russkii Khristianskii Gumanitarnyi Institut, [in Russian], URL www.ihst.ru/projects/sohist/books/luzin.pdf.

HEYTING, Arend [1936], Obzor issledovanij po osnovanijam matematiki, Translated by A.P. Yushkevich. Forward by A.N. Kolmogorov. Moscow-Leningrad: ONTI NKTP SSSR, [in Russian]. German original: Mathematische Grundlagenforschung, Intuitionismus, Beweistheorie, Berlin: J. Springer, 1934.

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KOLMOGOROV, Andreǐ N. [1925], O principe tertium non datur, Matematicheskij sbornik, 32, 646–667, [in Russian]. English translation: On the principle tertium non datur, in van Heijennort, J. (ed.) From Frege to Gödel, A Source Book in Mathematical Logic, 1879-1931, Harvard University Press, 1967. Reprinted in [Nikol'skij 1985, 45–68], URL www.mathnet.ru/links/ ffe370e498d5a44fddaf9ee09d0b27c8/sm7425.pdf.

—— [1932], Zur Deutung der intuitionistischen Logik, Mathematische Zeitschrift, 35(1), 58–65, doi: 10.1007/BF01186549.

KUSHNER, Boris A. [1973], Lekcii po konstruktivnomu matematicheskomu analizu, Moscow: Izdatel’stvo “Nauka”, [in Russian]. English translation by E. Mendelson Lectures on Constructive Mathematical Analysis, Providence: American Mathematical Society, 1984.

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—— [1954b], Teorija algorifmov [Theory of algorithms], Trudy matematicheskogo instituta im. V.A. Steklova, 42, 3–315, [in Russian], URL www.mathnet.ru/links/ 13a476d238e313f7a66ec80f1a961123/tm1178.pdf.

—— [1956], Ob odnom principe konstruktivnoj matematicheskoj logiki [On a constructive principle of mathematical logic], Trudy tret’ego Vsesojuznogo matematicheskogo s”ezda, 2, 146–147, [in Russian].

—— [1958], O konstruktivnyh funkcijah [On constructive functions], Trudy matematicheskogo institua im. V.A. Steklova, 52, 315–348, [in Russian], URL www.mathnet.ru/links/ b2dc4d7cdef827fa07f160497a2a6a78/tm1320.pdf.

—— [1962], O konstruktivnoj matematike [On constructive mathematics], Trudy matematicheskogo institua im. V.A. Steklova, 67, 8–14, [in Russian], URL www.mathnet.ru/links/ 80837f80d53ef16c770dd46a2757389c/tm1756.pdf.

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—— [1974g], O jazyke Яω| [On language ω|], Doklady Akademii Nauk SSSR, 215(1), 57–60, [in Russian]. —— [1987], Chto takoe konstruktivnaja matematika? (Vvedenie, Publikacija i predislovie N.M. Nagornogo) [What is constructive mathematics? (Introduction, Publication and preface by N.M. Nagorny)], in: Zakonomernosti razvitija sovremennoj matematiki, edited by M. I. Panov, Moscow: Nauka, 209–212, [in Russian].

MARKOV, Andreǐ A. & NAGORNYǏ, Nikolaǐ M. [1984], Teorija algorifmov, Moscow: Nauka, [in Russian]. English translation by Greendlinger, M., The Theory of Algorithms, Dordrecht; Boston: Kluwer, 2010.

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OLSZEWSKI, Adam, WOLEŃSKI, Jan, & JANUSZ, Robert (eds.) [2006], Church’s Thesis After 70 Years, Heusenstamm: Ontos Verlag.

WEYL, Hermann [1934], O filosofii matematiki, Moscow; Leningrad: Gostekhteorizdat, [in Russian]. Reprinted 2005. German original: Philosophie der Mathematik und Naturwissenschaft, 1927. 2nd edn., 1949. English translation: Philosophy of Mathematics and Natural Science, Princeton: Princeton University Press, 2009.

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YANOVSKAYA, Sofya A. [1936], Sovremennye techenija v burzhuaznoj filosofii matematiki, in: Sbornik statei po filosofii matematiki, edited by Sofya A. Yanovskaya, Moscow: Gos. uchebno- pedagogicheskoe izd., 84–96, [in Russian], URL http://ir.nmu.org.ua/bitstream/handle/ 123456789/102903/c75330a023e94791838d1c073b766a49.djvu?sequence=1&isAllowed=y.

ZASLAVSKIǏ, I. D. [1962], Nekotorye svojstva konstruktivnyh veshhestvennyh chisel i konstruktivnyh funkcij [Some properties of constructive real numbers and constructive functions], Problemy konstruktivnogo napravlenija v matematike. 2. Konstruktivnyj matematicheskij analiz, 67, 385–457, [in Russian], URL www.mathnet.ru/links/ 365aaf28b6c909187a6a7d3531820ca6/tm1760.pdf.

ZASLAVSKIǏ, I. D. & CEǏTIN, G. S. [1962], O singuljarnyh pokrytijah i svjazannyh s nimi svojstvah konstruktivnyh funkcij [Singular coverings and properties of constructive functions connected with them], Problemy konstruktivnogo napravlenija v matematike. 2. Konstruktivnyj matematicheskij analiz, 67, 458–502, [in Russian], URL www.mathnet.ru/links/ c205e0b68376378fef3887294d31ae06/tm1761.pdf.

NOTES

1. 1. Disputation, 2. Arithmetic, 3. Spreads and species, 4. Algebra, 5. Plane point species, 6. Measure and integration, 7. Logic, 8. Controversial subjects. 2. Often referred to as “the junior” in the mathematical literature, to distinguish him from his father, Andreǐ A. Markov (1856-1922), who is known for his contributions in probability theory, mathematical analysis and number theory. 3. This term was introduced by Markov during the second half of 1940’s. 4. Markov uses the word algorifm (with “f”) to denote “normal algorithm”, instead of the common Russian word algoritm (with “t”). 5. Markov objects also to Heyting’s definitions of measure and measurable region (in chapter 6) and suggests how own constructive reinterpretation of these concepts [Heyting 1956, 178]. 6. Sofya Yanovskaya was one of Yushkevich’s teachers in a gymnasium when the Yushkevich family returned to Odessa after 1917.

ABSTRACTS

The paper examines Andre A. Markov's critical attitude towards L.E.J. Brouwer's intuitionism, as is expressed in his endnotes to the Russian translation of Heyting's Intuitionism, published in Moscow in 1965. It is argued that Markov's algorithmic approach was shaped under the influence of the mathematical style and values prevailing in the Petersburg mathematical school, which is characterized by the proclaimed primacy of applications and the search for rigor and effective solutions.

Le présent article traite de l'attitude critique d'Andre A. Markov à l'encontre de l'intuitionnisme de L.E.J. Brouwer telle qu'elle se manifeste dans ses notes à la fin de la traduction russe de l'Intuitionnisme de Heyting, publiée à Moscou en 1965. On considère que l'approche algorithmique de Markov s'est développée sous l'influence du style mathématique et des valeurs régnant au

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sein de l'Ecole mathématique de Saint-Pétersbourg, qui est caractérisée par la primauté accordée aux applications et à la recherche de la rigueur et de solutions efficaces.

AUTHOR

IOANNIS M. VANDOULAKIS The Hellenic Open University, School of Humanities (Greece)

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The Fitness Landscape Metaphor: Dead but Not Gone

Stefan Petkov

1 Introduction

1 The concept of adaptive landscape was introduced by Sewall Wright, in the early stages of evolutionary synthesis between Mendelian genetics and Darwinian evolutionary theory. Very briefly, the concept presupposes that the interaction between the evolutionary forces and variation due to genetic factors can be represented in one unified framework as a graphic which shares some features with topographic maps; for instance, the fitness values of genetic combinations or genetic frequencies are gradated, and presented as peaks and valleys. Wright’s central idea was that a graphic produced in this manner could serve in exploration of the evolutionary dynamics.

2 However, the concept of adaptive relief was proven to be problematic and attracted a considerable critical attention. The critics of adaptive relief focused mainly on the fact that Wright had proposed its original concept as an illustrative supplement to his already developed mathematical model of how genetic drift and selection can cooperate to produce evolutionary change. But because of the oversimplified nature of the graphic, speculations based only on it and the concept of adaptive landscape led scientists to investigate pseudo-problems. Thus, according to the critics, the most sensible course would be to abandon the metaphor altogether in favor of some more strict formal investigations.

3 The proponents of the adaptive landscape metaphor, on the other hand, focused on the fact that the metaphor has been a base for plurality of interpretations some of which have overcome the difficulties of Wright’s first interpretation, or have been successfully applied to different evolutionary problems like the explanation of the Cambrian explosion [Marshall 2006] and the theoretical modeling of phenotypic variation [Niklas 1994].

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4 In this paper I suggest a semantic approach to the analysis of the functions of the landscape metaphor within evolutionary biology. It is important to make the clarification that the adaptive landscape is an umbrella term. It encompasses the adaptive landscape metaphor a metaphoric vocabulary used to interpret the mathematical models and the graphical representations, that illustrate some features of those models. My focus in this paper will be almost exclusively on this metaphoric vocabulary. I think that most of the analyses of the landscape metaphor mirror the three general views about the role of metaphors in science, namely: 1. Scientific metaphors are ornaments of already well-defined mathematical models. Being such an ornament, the landscape metaphor could be abandoned, without loss of content, in favor of more strict mathematical models. 2. Scientific metaphors play a heuristic function in the first stages of theory development but later become superfluous. As such the landscape metaphor could be abandoned, because the modern synthesis has already reached a more mature stage of development. 3. Metaphors are identical to the models that instantiate them, insofar as all scientific metaphors could be reduced to a set of analogies that could be specified in particular models. As such the landscape metaphor is reducible to a set of loosely based models.

5 However, none of these general views about scientific metaphors fit the case of the adaptive landscape metaphor. Thus by adopting them the critics of the metaphor fail to account for its primary function: to serve as a general unifying conceptual framework, which has greatly facilitated the synthesis and which still provides a basis for unifying heterogeneous evolutionary phenomena and explanations.

6 In order to clarify my point, I’ll first outline the history and the main interpretations of the landscape metaphor. Then I’ll present the general views about the role of metaphors in science. I’ll try to show that the main critical analyses of the landscape metaphor presuppose the general views about the role of metaphors in science, and as a result they overlook their function as a conceptual framework. Finally I’ll present an alternative to the general views about the function of scientific metaphors, and explain why it copes better with the case of the landscape metaphor. According to the view I wish to develop, the primary role of scientific metaphors is to set a unifying conceptual framework. That framework consists of a vocabulary for addressing a reality for which no appropriate descriptive tools have been known so far, and of a general heuristics which permits the unification of previously unrelated phenomena and explanations. As a result, I’ll propose, that a functional difference can be drawn between the scientific metaphors and models. Scientific metaphors are neither true nor false. Scientific models which are based on them can themselves be true or false, or adequate or inadequate representations of reality. The conceptual vocabulary is relatively independent from the models which are set forward by it.

2 The landscape metaphor: history and developments

7 Sewall Wright, publicly presented the landscape metaphor for the first time in 1932, during the 6th International congress on genetics. Wright was asked to present his ideas in a short form, and to keep his mathematical demonstrations at minimum, so he used the metaphor as an illustration to his already developed mathematical model [Wright 1932].

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8 However, the earliest known variant of his landscape metaphor appeared a year earlier (February 3, 1931) in a letter to Fisher [Provine 1986, 271-273].

9 In this letter Wright discussed his shifting balance theory of evolution, pointing out that the field of gene frequencies can be represented in a multi-dimensional space with an extra-dimension corresponding to fitness. He visualized the multi-dimensional space by the following two-dimensional graphic:

Figure 1: 2D adaptive relief, redrawn from Wright’s letter to Fisher — February 3, 1931, [Provine 1986, 272]

10 Wright explained the evolutionary factors that can draw a system of gene frequencies “uphill” (that is toward increased fitness), using the graphic. He outlined 4 factors: 1. Environmental change which is a change in the adaptive relief. 2. Mutations, creating new dimensions and occasionally new paths of advance uphill. 3. Random drift in small populations or exploration of adaptive relief. Incidentally, a population might stumble to a new positive genotype which will become fixed under selection, thus pushing the population uphill. 4. Subdivision of species into many small, not quite completely isolated groups.

11 One such group can be presented at point B. It will drift between A and C, because of the random sampling (genetic drift). Once it reaches the “slope” of C, the increased fitness will carry it uphill. This will lead to increased number of surviving offsprings and the population will become the major source of migrants to other groups. Since C is the highest peak, it will become the standard for this species. The key concepts of evolution, as envisioned by Wright’s shifting balance theory, were already in the letter presented in a rudimentary form with the help of the landscape metaphor. Thus at the next year’s congress of genetics, Wright merely articulated the metaphor in a more elaborated form.

12 There he famously presented the problem of evolution in the following way: The problem of evolution as I see it is that of a mechanism by which the species may continually find its way from lower to higher peaks in such a field. In order that this may occur, there must be some trial and error mechanism on a grand scale

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by which the species may explore the region surrounding the small portion of the field which it occupies. To evolve, the species must not be under strict control of natural selection. Is there such a trial and error mechanism? [Wright 1932, 360]

13 The answer which he gives is that the most favorable evolutionary scenario is subdivision of the species in small semi-isolated populations in which selection and genetic drift might co-operate providing conservation for the favorable genotypes and new genetic combinations which might be tested for their adaptive value.

14 Wright’s presentation was a great success and his metaphor became the core of one of the most important works for the synthesis: Dobzhansky’s Genetics and the origin of species [Dobzhansky 1937, 102-105]. Dobzhansky was a “field” biologist as opposed to Wright’s theoretical approach. These two scientists found convenient to use the “landscape” metaphor to communicate their own research. Their collaborative scientific work could be used as an example of the spirit of the synthesis as well as an illustration of the communicative role of the landscape metaphor.

15 The interpretations of the metaphor increased. Literally every major figure during the synthesis adopted some understanding of the adaptive landscape that fitted his views on evolutionary dynamics.

16 Fisher, for instance, adopted a single peak adaptive relief because he suspected that as the dimensions increase, the local peaks in lower dimensions will tend to become saddle points in higher dimensions. In this case, natural selection will be able to move the population to the global peak without any need for genetic drift or other factors. Even though, situations with a single global peak that can be reached by selection alone proved to be exception rather than the rule, the single peak-metaphor still remains a useful model for studying problems such as the levels and the structure of genetic variation maintained by mutation [Gavrilets 2004, 38].

17 The landscape metaphor played also an important unificatory role during the synthesis. This point could be exemplified by the work of Simpson who also used the metaphor in his Tempo and mode of evolution, but he interpreted the landscape not as constructed from genotypes or genetic frequency, but from phenotypic traits. His project was to unify (or reduce) paleontology with population genetics [Simpson 1944], [Gould 2002, 528-531]. His interpretation also might serve to exemplify the point that on the onset the landscape metaphor was not confined to a single model or theory but proliferated to other fields like paleontology.

18 However, Wright’s idea did not remain unproblematic. Wright used the concept to present an adaptive landscape populated by genetic combinations and genetic frequencies. He used the two variants of the adaptive landscape as interchangeable although they are not wholly mathematically compatible [Gavrilets 2004, 69-76].

19 Further theoretical studies of Wright’s model had also shown another problem. If the adaptive landscape contains peaks and valleys, the problem of peak-shift proves to be solvable only in very limited circumstances, thus it could not be the general mechanism of species formation as Wright envisioned it [Gavrilets 2004, 69-76].

20 In a more influential paper, Coyne, Barton & Turelli showed that the shifting balance theory does not have any compelling empirical support. On the contrary the authors claim that most of the cases which Wright interpreted as a support to his theory are better explained by Fisherman’s mass selection [Coyne, Barton et al. 1997, 664].

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21 However the falsification of the original shifting balance theory has not led to the abandonment of the adaptive landscape metaphor. And this fact supports the view that, the concept of adaptive landscape is largely independent from its particular interpretations.

22 In a recent study Sergey Gavrilets re-interpreted the concept of adaptive landscape in order to mend the flaws in Wright’s original model. He presented the adaptive relief as a multidimensional surface which could be graphically represented as a flat holey plane. In his variant, fitness is normalized between zero (nonviable) and one (viable). Thus the genotypes of equal or nearly equal fitness form a “net” through the genotypic space. The “holes” represent parts of the genotypic space where there are more densely situated deleterious mutations with fewer viable combinations among them. The process of species formation is presented as a movement on the neutral net. Because the simple shifts in the genotype will eventually lead to sexual isolation. Gavrilets’ variant overcomes the peak-shift problem which plagued earlier interpretations [Gavrilets 2004, 100-114].

23 The landscape metaphor did not remain confined only in population genetics. As we have already stated, one of its earliest incarnations was made by Simpson to designate phenotypic variation. This interpretation remains in circulation today and has been re- rejuvenated by the work of Niklas to model morphological diversity in plants [Niklas 1994].

24 Expounding on the work of Niklas, Marshall applies the concept of adaptive landscape explicitly as a conceptual framework which unifies in one consistent picture the existing explanations of Cambrian explosion [Marshall 2006, 355-384]. In short, he utilizes the phenotype variant of the adaptive landscape to demonstrate that the rapid diversification of forms is caused by the interaction between the variations due to the existing genetic basis for bilateral development, with the increased number of needs the organisms had to satisfy as a result from the development of complex ecological interactions, such as predation.

25 This short and by no means complete survey of the interpretations of the landscape metaphor is sufficient to demonstrate its rich history and its prolific applications to quite different problems within evolutionary biology.

26 The preliminary conclusion which we might draw is that all those interpretations would not be possible if the landscape metaphor was related only to Wright’s shifting balance theory.

27 The methodological critics of the adaptive landscape concept, however, presuppose that scientific metaphors are reducible to a set of analogies, or are mere ornaments facilitating understanding. Thus they focus on the problematic aspects of Wright’s notion of fitness landscape and his shifting balance theory or on the problems of constructing precise graphics of evolutionary mathematical models. The general conclusion which they draw, in most cases, is that the concept of adaptive landscape could be abandoned in favor of rigid mathematical models. I shall try to demonstrate that these views are misled by the general understanding about the functions of scientific metaphors. Thus my next task will be to overview the understandings about the functions of scientific metaphors that have dominated philosophy of science in the last years.

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3 Metaphors in science

28 According to the substitution view, which is one of the general views about scientific metaphors, metaphors have no serious place in scientific discourse. They can be used only as rhetoric ornaments, or for educational purposes. The reason behind it is that metaphorical statements are literally false thus expressing a deviation of meaning. The consequence is that they can’t be vigorously verified as declarative statements of facts. If metaphors are ever to be found in scientific texts, it must be possible in any moment to substitute them with literal paraphrases, without any loss of content.

29 With the fall of classical positivism, however, this view was abandoned in favor of the substantial view. The roots of the substantial view lie in the work of Max Black and it was later developed mainly by Richard Boyd and Marry Hesse. According to it, metaphors could have a positive place in science because: 1. They are introduced to address new aspects of reality which are the aim of the investigation and for which no literal descriptions yet exist; thus metaphors fill “vocabulary gaps”. 2. They are a source of analogies which can be precisely investigated by setting them in scientific models.

30 The position of Max Black [Black 1993, 19-42] is that the primary function of scientific metaphors is heuristic. The metaphor lets its referent to be investigated as a projection of implications common for the literal meaning of the phrase. In this way, some possible features of similarity and analogy between the second and the primary subject of the metaphor become apparent. Since those features might be typically in the background when the object is referred to by the literal expression, or there might be no suitable literal expression to begin with, metaphors can give an irreplaceable insight on how things really are.

31 The drawback is that the complex of common implications is not limited in any way, so the metaphor trades its fixed meaning for open-endedness. According to Black, this proves to be a limitation in scientific discourse because its central aim is exactly the opposite: the formation of empirically testable sentences. In this case the conclusion that Black draws is justified: metaphors can be used only in the initial phases of theory construction as a heuristic tool. Later they must be replaced by strict testable models.

32 Richard Boyd builds up on that but he emphasizes that there are important cases of metaphors in relatively mature sciences. His thesis is that some metaphors have a theory constructive function [Boyd 1993, 481-533]. He tries to find what kind of mechanisms might let metaphors to persist in theory development beyond the initial heuristic phase.

33 Boyd suggested that metaphors are usually born as a consequence of an “informed guess”, a suggestion of analogies between a known system and the system which is to be investigated. Thus metaphorical open-endedness is not always a limitation. It expresses the need for precise fit between scientific language and the causal structure of the world. Boyd’s position is that the investigation of analogies and similarities will eventually reveal the real categories of phenomena, which will be expressed as metaphor’s open-endedness is exhausted. As scientific research progresses, the metaphor “dies”, because all the aspects of similarity and analogy have been explained. The result is a precise description of the phenomena via the vocabulary introduced initially by the metaphor.

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34 It is important to note that scientific metaphors can also be rejected on the basis that the aspects of similarity and analogy relevant to the theory are to be found incorrect, or that the metaphor will be found to have no unique referent. We may conclude that Boyd’s view is that metaphors have substantial heuristic role.

35 The addition which Marry Hesse [Hesse 1970] does to the substantial view is that the metaphor’s function is reducible to that of scientific models. In turn, models can be summarized as a list of positive, negative, and neutral analogies. The negative analogies are features of dissimilarity, positive analogies are features of similarity, and neutral analogies are features of phenomena that are yet to be investigated. Scientific models owe their predictive power to the latter.

36 In the next paragraph I demonstrate that the present views are mirrored by the methodological critiques of the landscape metaphor and that’s why these critiques could not adequately account for the actual usage of the landscape metaphor in evolutionary biology. According to my analysis, the metaphor has been mainly used as a conceptual framework facilitating the unification of heterogeneous evolutionary phenomena. This function could be explained only if we accept the idea that scientific metaphors do not relate to a fixed secondary meaning. The “open-endedness” of the landscape metaphor made possible the advance of new interpretations after the falsification of the primary model of Sewall Wright.

4 The critics of the landscape metaphor

37 The first serious critique of the landscape metaphor mirrored the substitution view. It was made by Provine in his biography of Wright [Provine 1986, 308-317]. There he defended the idea that the only function the adaptive landscape concept have is to facilitate understanding of Wright’s formal model. But since there exist at least two variants of the metaphor that can be expressed with the same graphical representation and discussed in the same terms (the adaptive landscape constructed by grading genetic combinations and genetic frequencies) and those variants are not completely mathematically equivalent, the metaphor taken by itself leads to a confusion.

38 Provine argued further that the graphical representations of the adaptive landscape populated by genetic combinations are even more confusing, because the genetic combinations are discrete entities, and the graphic represents them on a continuous surface. Thus he concluded that since Wright’s shifting balance theory is already well- defined in precise mathematical terms, it does not depend on the usefulness of the landscape metaphor.

39 This critical position is further developed by Jonathan Kaplan. According to him, Wright’s main idea was that the interpretations based on the graphics alone can help to reach important conclusions about evolutionary dynamics [Kaplan 2008, 627]. However, the errors in constructing the graphic of the adaptive landscape and the verbal speculation based on the metaphor led biologists to investigate pseudo-problems like the “peak-shift problem”.

40 Kaplan also discussed the model of Gavrilets, which aims to mend the flaws in Wright’s shifting balance theory. He notes that interpretations based solely on the graphics or on verbal speculations with his interpretation could also lead to erroneous conclusions,

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because the graphics and the supporting concepts of the adaptive landscape again are oversimplifications of his otherwise rigid formal model. Thus he concludes also that: it is time to give up the pictorial metaphor of the landscape entirely and rely instead on the results of formal modeling, however difficult such results are to understand in “intuitive” terms. [Kaplan 2008, 625]

41 A more positive interpretation of the adaptive landscape as a rhetoric tool is due to Jean Gayon [Gayon 1998, 321-355]. According to him the metaphor in its original form has been developed by Wright mainly, as a rhetoric tool, to criticize Fisher’s fundamental theorem. Wright never intended the “adaptive landscape” as a center to a rigidly defined mathematical model. Thus he never precisely defined the “peaks” in a parameter space, which he expressed as formed both of “gene combinations” and “gene frequencies”. Wright’s main aim was to show that since multiple adaptive peaks could represent multiple possible adaptive optima, Fisher’s fundamental theorem explained only the behaviour of the populations when they are already in the vicinity of an adaptive peak. Thus Wright’s own shifting balance theory presented a more general view of speciation.

42 The critique of the metaphor based on the idea that it has only ornamental value could be met by the actual history of the metaphor in which, as we have seen, the concept received multiple interpretations some of which are not related directly to the graphical representations and have a clear explanatory power. For instance, in Marshall’s analysis of the causes for the Cambrian explosion, the concept of adaptive landscape is used to order the existing explanations in one unified framework. Moreover, the concept itself could not be erroneous or flawed; but its interpretations in particular models could be good or bad representations of the evolutionary dynamics. Finally the notions of “peaks”, “valleys”, “random walks”, “changes in the relief” in fact could be defined in a mathematically precise matter, as recent formal research in evolutionary algorithms shows [Richter 2010, 409-447].

43 The idea that scientific metaphors function as heuristic tools in the case of the landscape metaphor is exemplified by the analyses of Michael Ruse and Massimo Pigliucci.

44 According to Ruse, the concept of adaptive landscape is not necessarily related to Wright’s mathematical model because it has found numerous interpretations during the synthesis [Ruse 1996, 75]. These interpretations, in turn, were possible because of the metaphor’s open-endedness, which served as a heuristic basis for inferring testable hypotheses.

45 In a more recent work Pigliucci makes an overview of the interpretations of the metaphor, having in mind the same idea—that the metaphor’s interpretations should be judged according to their heuristic value; but the actual tools that bring significant scientific results are the underlined mathematical models [Pigliucci 2013, 26-32].

46 The view of Max Black as an approach to the functions of the landscape metaphor is more susceptible to its many interpretations. As a result the analysis of Ruse and Pigliucci is historically more accurate. But by focusing only on the heuristic function they overlook the fact that the concept of adaptive landscape provides a vocabulary and an approach in modeling and explaining the complex phenomena of evolution.

47 Both views, that the adaptive landscape concept is a heuristic tool or a rhetoric ornament, have in common the idea that the underlined mathematical models are somehow the most important vehicle of scientific progress. This idea disregards the

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fact that there is no other way to make the assumptions and consequences of mathematical models intelligible, but using additional concepts, explaining their precise place and meaning in the general theory. Any mathematical model in evolutionary biology represents some relationship between magnitudes of known evolutionary factors. Without a general conceptual framework which unites them, the mathematical models can’t be clarified and united. The concept of genotype space which is the essence of the landscape metaphor is an example of such a framework. It presents a pattern for the analysis of the relationships between the forces which “shape” the genotype space—natural selection, genetic drift, mutation, migration, sexual isolation etc. In turn, those relationships can be presented more rigidly by landscape based models.

48 The third approach treating scientific metaphors as a source of analogies on which models are based finds place in the work of Anya Plutynski, Robert Skipper, Michael Dietrich and Brett Calcott.

49 Anya Plutynski explicitly bases her analysis on the Hesse’s views about scientific metaphors [Plutynski 2008, 617]. Plutynski defends the position that a complex phenomenon as species formation could be investigated only with the help of idealized models which focus only on some of the relevant factors. The landscape metaphor presented such an approach, and has played a heuristic function during the synthesis, because it proposed an analogy which could be tested. The peak shift problem was rooted in the similarity between adaptive landscape and geographic relief. It presupposes the existence of adaptive peaks which require the populations to traverse “areas” of lower fitness or adaptive valleys. The analogy between the fitness landscape and the geographic relief is obvious: in mountains we must always pass valleys in order to reach new peaks.

50 However the peak shift problem proved to be based on a negative analogy. The reason why the landscape metaphor was not falsified, according to Plutynski, is that Gavrilets’ variant still provides new “neutral analogies”—the dynamics on his neutral relief could prove to bring new insights on evolution. The conclusion she makes is that since evolutionary biology at present does not have a new better approach to investigate the relationship between individual adaptation and genetic frequencies, the claims for the removal of the metaphor are hastened.

51 This point is further exemplified by the work of Robert Skipper & Michael Dietrich. According to them the adaptive landscape metaphor serves a heuristic function, which depends on the analogy with actual hilly landscapes and their representation as topographical maps [Skipper & Dietrich 2013, 18]. This in turn permits the graphic representation to have a dual function: a didactic function for the underlined mathematical model and a heuristic function for imagining how the represented system might behave [Skipper & Dietrich 2013, 23].

52 This type of analysis has one limitation: by focusing on analogies, we disregard the fact that some of the successful interpretations of the adaptive landscape concept are not at all based on examination of literal similarities. Gavrilets’ variant does not display any meaningful metaphoric similarities. His interpretation of the adaptive landscape concept is defined mostly by his formal model. Thus the metaphoric terms which he employs as holes and neutral networks do not designate analogies but are details of his formal model. The metaphor itself does not provide a correct approach or accurate description of evolutionary phenomena based on analogies and similarities.

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53 In this case it seems possible to examine the landscape metaphor as a group of weakly related models and to avoid the whole semantic debate about the function of scientific metaphors. The position of Brett Calcott follows similar ideas. According to him, the landscape metaphor is simply a family of models which address different evolutionary problems. In his view, no interpretation could claim universal validity or application [Calcott 2008, 640]. The idea that adaptive landscape models have a limited validity is close to the idea that I wish to develop in the next paragraph: that the landscape metaphor functions as a unifying conceptual framework. According to Calcott, the only difference between scientific models and scientific metaphors is based on the degree of accuracy in defining the meaning of scientific metaphors and defining what models signify. Since both can be more or less precisely defined, the difference between them could be neglected. Thus the landscape metaphor could be analyzed as a group of loosely based models. However, we should bear in mind that if evolutionary models use radically different conceptual apparatuses, their unification under a general theory will be very difficult. Calcott’s analysis could serve to show that models aim at solving particular problems. The common conceptual vocabulary that is their base has a wider unificatory role.

5 The landscape metaphor as a conceptual framework

54 As we have seen so far, all the methodological critiques of the landscape metaphor presuppose one or another general view about scientific metaphors. Neither of the adopted general views, however, can adequately account for the history of the concept of adaptive relief or for its current uses.

55 The radical shifts in interpretation concerning different problems like population dynamics (Wright’s original study), species formation (Gavrilets) and phenotypic variation (Simpson, Niklas and Marshall) are possible only if the concept of “fitness landscape” is taken to be relatively independent from the model which was first exemplified with its help. This in turn signifies that the concept of adaptive landscape is not confined to a rhetoric figure which illustrates a formal model, nor to a particular heuristic pattern, or to a set of testable analogies.

56 The reason for the prolific use of the metaphor in modern evolutionary theory, I think, is that the concept of adaptive landscape provides an invaluable unifying conceptual framework which could be specified to accommodate various evolutionary models which unify several previously separately studied evolutionary phenomena in order to investigate their relationships. Moreover, the concept was used in its more loose non- mathematically defined form to construct unified explanations of concrete evolutionary episodes like the evolution of the horse [Simpson 1944, 89-93] and the Cambrian explosion (Marshall). The latter are additional examples of metaphor’s more general usage which is relatively independent from any concrete mathematical models.

57 Further evidence in support to this view is the recent theoretical research into evolutionary algorithms [Richter 2010], which has shown that the adaptive landscape could be defined in a mathematically precise matter in its more complex form as a dynamic adaptive landscape. Thus the theoretical research in dynamic systems could be integrated successfully within the adaptive landscape framework. Of course models using evolutionary algorithms on the adaptive landscape remain largely theoretical but

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their development might be a step in the right direction of the analysis of the evolutionary dynamics of real biologic populations.

58 Finally a recently published volume [Svensson & Calsbeek 2013] dedicated to the many applications of the adaptive landscape, has made plain the fact that the adaptive landscape has not outlived its usages and it is perhaps an indispensable element in some fields of evolutionary biology such as evolutionary genetics, ecological theory of adaptive radiation and ecological speciation.

59 For our purposes however the history of the development of the adaptive landscape metaphor can be used to draw a new conclusion about some theory-constructive scientific metaphors. Their primary function is to set a unifying conceptual framework. That framework consists of a vocabulary for addressing a reality for which no appropriate descriptive tools have been known so far; and of a general heuristics which permits unification of previously unrelated phenomena and explanations. This view implies that there is a functional difference between scientific metaphors and models. Scientific metaphors are neither true nor false. Scientific models which are based on them can themselves be true or false, or adequate or inadequate representations of reality. That means that the conceptual vocabulary is relatively independent from the models which are set forward by it.

60 The landscape metaphor is a good example for such a conceptual framework. It was introduced during the early stages of the evolutionary synthesis when it served as a heuristic tool. But it did not only provided a graphical representation and a model of evolutionary dynamics but a common dictionary for describing relations between evolutionary phenomena (such as variation and inheritance) which were previously treated as unrelated by the early and confronting theories of genetics and evolutionary biology.

61 Keeping such a common framework is important. If we use several unrelated models each with its specific vocabulary addressing different evolutionary problems such as morphological diversity and species formation, the unification under one theory will be harder, if possible at all. But if we use a common conceptual framework to interpret all the different models that have been suggested, the achievement of unification and consensus will be significantly easier.

BIBLIOGRAPHY

BLACK, Max [1993], More about metaphor, in: Metaphor and Thought, edited by A. Ortony, Cambridge, MA: Cambridge University Press, Cambridge Books Online, 2nd edn., 19–41, http:// dx.doi.org/10.1017/CBO9781139173865.004.

BOYD, Richard [1993], Metaphor and theory change: What is “metaphor” a metaphor for?, in: Metaphor and Thought, edited by A. Ortony, Cambridge, MA: Cambridge University Press, Cambridge Books Online, 2nd edn., 481–532, http://dx.doi.org/10.1017/CBO9781139173865.023.

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CALCOTT, Brett [2008], Assessing the fitness landscape revolution, Biology & Philosophy, 23(5), 639– 657, http://dx.doi.org/10.1007/s10539-008-9127-9.

COYNE, Jerry, BARTON, Nicholas, & TURELLI, Michael [1997], Perspective: A critique of Sewall Wright’s shifting balance theory of evolution, Evolution, 51(3), 643–671.

DOBZHANSKY, Theodosius [1937], Genetics and the Origin of Species, New York: Columbia University Press.

GAVRILETS, Sergey [2004], Fitness Landscape and the Origin of Species, Princeton: Princeton University Press.

GAYON, Jean [1998], Darwinism’s Struggle for Survival Heredity and the Hypothesis of Natural Selection, Cambridge: Cambridge University Press.

GOULD, Stephen J. [2002], The Structure of Evolutionary Theory, Cambridge, MA: Belknap Press.

HESSE, Marry B. [1970], Models and Analogies in Science, Notre Dame: University of Notre Dame Press.

KAPLAN, Jonathan [2008], The end of the adaptive landscape metaphor?, Biology & Philosophy, 23(5), 625–638, http://dx.doi.org/10.1007/s10539-008-9116-z.

MARSHALL, Charles R. [2006], Explaining the Cambrian “explosion” of animals, Annual Review of Earth and Planetary Sciences, 34(1), 355–384, http://dx.doi.org/10.1146/annurev.earth. 33.031504.103001.

NIKLAS, Karl J. [1994], Morphological evolution through complex domains of fitness, Proceedings of the National Academy of Sciences, 91(15), 6772–6779.

PIGLIUCCI, Massimo [2013], Landscapes, surfaces, and morphospaces: What are they good for, in: The Adaptive Landscape in Evolutionary Biology, edited by E. Svensson & R. Calsbeek, Oxford: Oxford University Press, 26–38, http://dx.doi.org/10.1093/acprof:oso/9780199595372.003.0003.

PLUTYNSKI, Anya [2008], The rise and fall of the adaptive landscape?, Biology & Philosophy, 23(5), 605–623, http://dx.doi.org/10.1007/s10539-008-9128-8.

PROVINE, William B. [1986], Sewall Wright and Evolutionary Biology, Chicago: University of Chicago Press.

RICHTER, Hendrik [2010], Evolutionary optimization and dynamic fitness landscapes, in: Evolutionary Algorithms and Chaotic Systems, edited by I. Zelinka, S. Celikovsky, H. Richter, & G. Chen, Berlin; Heidelberg: Springer, Studies in Computational Intelligence, vol. 267, 409–446, http://dx.doi.org/10.1007/978-3-642-10707-8_13.

RUSE, Michael E. [1996], Are pictures really necessary? The case of Sewall Wright’s “adaptive landscapes”, in: Picturing Knowledge Historical and Philosophical Problems Concerning the Use of Art in Science, Toronto: University of Toronto Pres, 303–375.

SIMPSON, George G. [1944], Tempo and Mode in Evolution, New York: Columbia University Press.

SKIPPER, Robert A. & DIETRICH, Michael R. [2013], Sewall Wright’s adaptive landscape: Philosophical reflections on heuristic value, in: The Adaptive Landscape in Evolutionary Biology, edited by E. Svensson & R. Calsbeek, Oxford: Oxford University Press, 16–25, http://dx.doi.org/10.1093/ acprof:oso/9780199595372.003.0002.

SVENSSON, Erik & CALSBEEK, Ryan [2013], The Adaptive Landscape in Evolutionary Biology, Oxford: Oxford University Press.

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WRIGHT, Sewall [1932], The roles of mutation, inbreeding, crossbreeding, and selection in evolution, in: Proceedings of the 6th International Congress of Genetics, 356–366.

ABSTRACTS

In this paper I present a semantic approach to the analysis of the function of the landscape metaphor within evolutionary biology. The concept of adaptive landscape has drawn a considerable attention in recent philosophy of biology. Most writers have treated the concept in one of the following ways: as a heuristic tool, as an intrinsic part of robustly defined mathematical models, or as a definable set of analogies on which models are based and tested. All these views lead to the conclusion that the value of the landscape metaphor depends only on the success of the models, which the metaphor underlies, to adequately represent evolutionary dynamics. I have tried to show that this conclusion, and respectively, the views which imply it, do not account for important episodes from the history of the landscape metaphor. These views rather stem from the general views, in philosophy of science, about the role of metaphors in scientific theories. The semantic analysis which I propose reveals that the concept of adaptive reliefs’ primary function during the evolutionary synthesis has been to serve as a general unifying conceptual framework which has made possible the theoretical reconciliation of heterogeneous empirical phenomena. From this perspective, the landscape metaphor is a linguistic theoretical tool which should not be abandoned (and in fact has not been abandoned) after the falsification of the models which have been built and interpreted by means of the metaphor.

Dans cet article, je présente une approche sémantique de l’analyse de la fonction de la métaphore du paysage dans la biologie de l’évolution. Le concept de paysage adaptatif a suscité une attention considérable dans la philosophie de la biologie récente. La plupart des auteurs ont considéré ce concept de l’une des deux manières suivantes: en tant qu’outil heuristique, comme partie intrinsèque de modèles mathématiques robustes, ou comme un ensemble définissable d’analogies sur lesquelles les modèles sont basés et testés. Chacune de ces visions conduit à la conclusion que la valeur de la métaphore du paysage dépend seulement du succès des modèles que sous-tend la métaphore, en vue de représenter adéquatement la dynamique de l’évolution. J’essaie de montrer que cette conclusion, ainsi que les visions qui y conduisent, ne tiennent pas compte d’épisodes importants dans l’histoire de la métaphore du langage. Ces visions proviennent plutôt de thèses générales, en philosophie des sciences, quant au rôle des métaphores dans les théories scientifiques. L’analyse sémantique que je propose met en lumière le fait que la fonction première du concept de relief adaptatif, au cours de la synthèse évolutionniste, a été de servir de cadre général d’unification conceptuelle, qui a rendu possible la conciliation de phénomènes empiriques hétérogènes. De ce point de vue, la métaphore du paysage est un outil linguistique-théorique qui ne doit pas être abandonné (et qui ne l’est de fait pas) suite à la falsification des modèles construits et interprétés au moyen de la métaphore.

AUTHOR

STEFAN PETKOV Institute of Science, Technology and Society, Tsinghua University (China)

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Cartesian Forces in a Soulless Physics

Zuraya Monroy-Nasr

1 Introduction

1 Rene Descartes’ radical dualism within the domain of metaphysics has fundamental consequences for his physics. Descartes intended to establish a certain and quantitative knowledge about the physical world. For this purpose, with his ontological dualism he drove souls, spirits or forces away from the material world. From his dualist conception, Descartes was able to construct an explanation on the physical world where its laws had to be expressed in terms of behaviors of material bodies, as mechanical regularities. Descartes was seeking to eliminate substantial forms, as well as final causes, both of which were deeply rooted in scholastic philosophy.

2 Descartes used the term “force” as a clear and differentiated concept, moving away from mentalist speculation or occult qualities that surrounded this concept. Nevertheless, some contemporary scholars have considered that Descartes, in some passages of The World and the Principles of Philosophy, expressed himself as if the forces described were “real” properties of the bodies. Against these interpretations, I will argue in this paper in favor of Cartesian dualism’s coherence, making use of a little- known notion of force proposedby Descartes.

2 Mechanics and forces in Cartesian physics

3 In October 1637, Descartes wrote a brief treatise on mechanics, due to the express request of his friend Huygens. In the introductory letter of the treatise, Descartes confesses to the solicitor that he has never felt less willing to write than in that moment. He complains about the lack of time, in part caused by the preparation of the Discourse’s publication and he says: White hairs are rapidly appearing on my head, which brings it home to me that the only thing I should be devoting myself to is ways of slowing down their growth.1

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That is what I am now doing. I am trying energetically to make up for my lack of observational data.2 This task takes up so much of my time that I have resolved to concentrate on this alone; I have even laid aside all work onmy World, so that I shall not be tempted to put the finishing touches to it. For all that, I am sending you the lines you requested, seeing especially that you only asked for three sheets [...] [AT I 434; CSM-K III 66].3

4 Next, Descartes presents “An account of the machines by means of which a small force can be used to lift heavy weights” or Traité de la Mécanique.4 There, he speaks about how the invention of machines is based solely upon the principle that the same force that can lift any given weight, say a 200-pound weight lifted to a foot’s height, may lift 400 pounds to half a foot’s height, and so on. [AT I 435–436; CSM-K III 66–67].

5 The principle Descartes is describing anticipates a term that does not exist yet: the physical notion of “work”. It’s important to emphasize that Descartes not only speaks of force but of the “required action needed [...] to produce an effect” cf. [A I 802, note 1]. Certainly, Descartes says that this principle must be accepted when it is considered that, the effect must always be proportional to the action which is necessary to produce it. Thus, if in order to lift a certain weight to a height of one foot we are required to employ a force which can raise a 100-pound weight to a height of two feet, then the said weight must be 200 pounds. [AT I 436; CSM-K III 67]

6 In the Treatise, Descartes presents some examples of machines like the pulley, the inclined plane, the wedge, the cog-wheel, the screw, and the lever; describing how they act in order to achieve the desired effect. In all these cases, the author continually uses the term “force” when referring to the action needed in order to sustain the weights under consideration.

7 I will not try to describe the mechanisms detailed by Descartes. What interests me is the examination of the senses in which the word “force” is used. I say senses in plural because as we will see, this term is equivocal. Henri Bouasse noted two meanings to the word force that “do not alternatively effort and work” [Bouasse 1895, 34].5 It should be mentioned that in the “Account” that Descartes sent to Huygens, he does not distinguish clearly the characteristics of either effort or work in the term “force”. “Effort” is a term that does not to include the idea of displacement in space, while work implies the notion of displacement, cf. [A I 805, note 1]. For Bouasse, this may apparently obscure the meaning of “force”. Nonetheless, this author thinks that Descartes expresses more clearly “the fact that work is measured by the productof a force times a displacement in space” [A I 805, note 1]. In contemporary terms [Tippens 2002, 173], Cartesian force would correspond to the notion of work, where: Work = force × displacement.

8 The distinction between “effort” and “work” may not be expressed through the proper terminology by Descartes. However, he did see the difference between both concepts. A few months later, in 1638, in a letter to Mersenne, Descartes exemplifies this distinction when referring to “the force that serves to elevate a weight to a determined height and the force that a nail needs to sustain a 100-pound weight”.

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3 Forced criticism

9 Within Descartes’ “Account” we observe that although there may be more than one sense to the term “force”, its use stands away from mentalist speculations or occult qualities that enveloped the concept in ancient and medieval traditions.

10 If incorporeal forces were present in the Cartesian matter, this would mean that there is no substantial distinction. In other works, I have procured the demonstration of how Cartesian dualism justifies the knowledge of the physical world by means of two aspects: 1) epistemologically, the incorporeality of the mind is necessary to establish certainty and truth in our knowledge and 2) ontologically, the radical distinction between thought and matter is indispensable in order to conceive Cartesian physic’s proper object: matter who’s essence is extension, cf. [Monroy-Nasr 2002].

11 For Max Jammer, at Descartes’ time there were two possibilities, either conceive force as the cause of change of motion, or to abolish the notion of force altogether. According to Jammer, Descartes chose the latter: he rejected the existence of force [Jammer 1957]. The main reason for this rejection would be that Cartesian dualism could not coexist with the traditional notion of force: His absolute dichotomy of existence into pure matter and pure spirit seemed to him incompatible with the assumption of force in matter or exerted by matter, since force, in his view, is still a somewhat psychic notion. Matter has to be divested of all spiritual constituents, of all inherent forms or tendencies. Only extension and external motion are its characteristics. [Jammer 1957, 103]

12 Jammer illustrates Descartes’ explanation of the physical process of free fall without any reference to attractive forces, with a letter that Descartes wrote to Mersenne in November 13, 1629 [AT I 71, CSM-K III 9] quoted by [Jammer 1957, 104]. Examples like these lead Jammer to the conclusion that The concept of force in Descartes’ view had no place in his physics, which was to employ exclusively mathematical conceptions. [Jammer 1957, 105]6

13 This author recognizes the importance of Descartes’ affirmation in the Principles, Part II, § 64, where Descartes says that The only principles which I accept, or require, in physics are those of geometry and pure mathematics; these principles explain all natural phenomena, and enable us to provide quite certain demonstrations regarding them. [AT IX-2 101–102; CSM I 247]

14 In turn, Edward Slowik points out some passages where Descartes “spoke out against the strange marriage of soul and matter” [Slowik 2002]. Slowlik recognizes that Descartes clearly and succinctly affirms that the scholastic hypothesis regarding this is unintelligible and inadequate as a methodological approach to an explanation of natural phenomena. In Descartes’ words from The World: If you find it strange that in explaining these elements I do not use the qualities called “heat”, “cold”, “moisture” and “dryness”—as the philosophers do—I shall say to you that these qualities themselves seem to me to need explanation. Indeed, unless I am mistaken, not only these four qualities but all the others as well, including even the forms of inanimate bodies, can be explained without the need to suppose anything in their matter other than the motion, size, shape, and arrangement of its parts. [AT XI 25–26; CSM I 89]

15 Nevertheless, says Slowik, the exhaustive studies of The World “reveal a curious and intractable qualitative bent” [Slowik 2002, 53]. Slowik exemplifies this with few early affirmations where it seems that Descartes understands force as a “power” that an

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individual, material object possesses. However, Slowik recognizes that Cartesian language is “far removed from the overt mind-influenced speculation of the scholastics”, which Slowik exemplifies with the impetus theory [Slowik 2002, 54].

16 The main problem is found in the Second Part of the Principles § 39, in the second law of nature where Descartes says that “all motion is in itself rectilinear; and hence any body moving in a circle always tends to move away from the center of the circle which it describes” [AT IX-2 85; CSM I 241]. Based on this principle and following the examination of centrifuge movement, Slowik mentions that movements and trajectories are described with expressions such as “the body desires to follow a straight line away from the center of its circular trajectory”, “the tendency of the object to continue along its circular path” and “there can be strivings toward diverse movements in the same body [...]” [Slowik 2002, 54].7 This author considers that these expressions may be vestiges of a former scholastic formation.

17 A brief digression may allow us to better comprehend how Descartes conceives the motion of bodies. Let us remember that in Chapter VII of The World, Descartes enunciated three laws of nature: 1. Each individual part of matter continues always to be in the same state so long as collision with others does not force it to change that state. [AT XI 37; CSM I 93] 2. When one body pushes another it cannot give the other any motion unless it loses as much of its own motion at the same time; nor can it take away any of the other’s motion unless its own is increased by as much. [AT XI 41; CSM I 94]. 3. When a body is moving it tends always to continue moving along a straight line. [AT XI 43– 44; CSM I 96].8

18 These fundamental laws are considered as true a priori principles, based on God’s own immutability. God’s immutability, aside from its fundamental role in the derivation of movement laws, has one very interesting consequence, which is shown by Dennis Des Chene. In the Principles, Part II § 36, Descartes tells us that God’s perfection involves not only being immutable in himself, but also his operating in a manner that is always utterly constant and immutable. There are some changes whose occurrence is guaranteed either by our plain experience or by divine revelation. [AT IX-2 61; CSM I 240]

19 For Des Chene, when Descartes says in the first law, in § 37, that a simple and undivided thing “never changes except as a result of external causes”, this follows from § 36 where he maintains that plain or “ ‘evident experience’ does not require us to postulate any internal principles of change in bodies” [Des Chene 1996, 316]. The only thing experience requires us to suppose is that “body is res extensa, and extension contains no principle of change. We then have no reason to suppose that God’s action will change” [Des Chene 1996, 316]. God’s immutability is the reason for supposing it will not.

20 Now, although the first law is applied to every state of matter, for the topic that is of our interest the third law carries more weight. Let us remember that in the Principles there is a different order to the presentation of its laws of nature. In Part II, § 39, this law appears in a newly formulated way and as second (not third) law. Here, it reads that: “all motion is in itself rectilinear; and hence any body moving in a circle always tends to move away from the centre of the circle which it describes” [AT IX-2 85; CSM I 241].

21 Ferdinand Alquié clarifies what he considers a frequent confusion regarding the laws of movement due to the aforementioned change in their presentation. Because the first

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two laws enunciated in the Principles constitute the so-called “Principle of inertia”, these are often confounded. This is because when it is said that a body is incapable of putting itself in motion or modifying itself, we understand that neither its speed nor direction can be altered. Alquié says that Descartes, on the contrary, separates quantity of movement and its direction, which leads him to enunciate two laws. However, modern physics mashes them into one and Descartes’ third law (§ 40) is not accepted. So, for Descartes, the effective movement of each material particle depends upon: 1) the ensemble of forces that determine it, forces that in their majority belong to neighbor particles, and not to the particle under consideration and 2) the force strictly pertaining to the considered particle; in this case and according to the effect of this force, movement is always rectilinear, but external forces can derail it from its essential direction, cf. [A III 187–188, note 3]. After this clarification, we must yet see if in the particle’s own force Descartessignals something that may be considered as the “desire”, the “power”, the “tendency” or the “real quality” that moves the part, according to expressions mentioned by Slowik.

22 Daniel Garber considers that in order to comprehend the Principle’s second law on rectilinear movement, there must first be full comprehension on what Descartes means by “tendency” or “inclination”. First, Garber refers us to a passage from The World where Descartes asserts that: When I say that a body tends in some direction, I don’t want anyone to imagine on account of that it has in itself a thought or a volition that pushes it there, but only that it is disposed to move in that direction, whether it really moves or whether some other body prevents it from moving [AT XI 84]9

23 Garber also reminds us that the same is expressed in Part III of Principles, in § 56, where Descartes is referring to certain parts that have the inclination or “strive” to stay away from the centres around which they revolve and explicitly clarifies that “it should not be thought that I am implying that they have some thought from which this striving proceeds. I mean merely that they are positioned and pushed into motion in such a way that they will in facttravel in that direction, unless they are prevented by some other cause” [AT IX-2 131; CSM I 259].

24 For Garber, Descartes chose to express the second law in terms of tendencies rather than more directy in terms “of a state of body that persists conditional on a lack of interference” [Garber 1992, 220], given that in the Cartesian plenum the condition of noninterference “can never be met” [Garber 1992, 220]. In effect, for Descartes the void does not exist, everything is full and all bodies or parts of a body, in order to move, must push another. The space that one leaves is occupied by other and therefore all movements must be circular [AT IX-2 81; CSM I 237].

25 Lastly, I would like to briefly mention Alan Gabbey’s interpretation. He has also considered that Descartes expresses himself in some passages of The World and The Principles as if the forces to which he refers to were “real properties” pertaining to the bodies.10 For example, Gabbey mentionsthat on The Principles, Part II, § 43, Descartes speaks of “the nature of the power which all bodies have to act on, or resist, other bodies” [AT IX-2 88–89; CSM I 243–244].

26 In this principle’s explanation Descartes insists on emphasizing that this force consists of the fact that everything persists in the same state, as was established in the first law. This way, what is joined to one thing has the power of resisting separation from it; and that which is separated has the power to remain separated. Also, what is at rest has the

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power to remain at rest and as a consequence resists to anything that may make it change. Gabbey interprets these expressions of resistance or persistence as an attribution of real properties to bodies.

27 This last principle contains several elements that are worth highlighting, but for the briefness of this exposition I will only mention that here we find the new idea that movement and rest are two states of matter that follow the same legality. In this principle, Descartes provides elements that explain the cohesion between bodies. This cohesion arises from the idea that every part of a body possesses a force of rest, not as an occult or immaterial quality, but as the property of staying in that state until an exterior force, by action of an external body, separates the parts that are joint, cf. [A III 194, note 1].

4 Conclusion

28 In spite of the textual evidences about Descartes’ exclusion of terms such as “souls”, “spirits” and other incorporeal entities hidden in matter, there is a certain persistence of interpretations by specialists that find expressions that indicate the presence of powers or non material forces in Cartesian physics.

29 Therefore, it is important to make sure that incorporeal forces are absent in the nature of matter, because their presence would undo the Cartesian dualist metaphysics. Ontologically, this would mean that there is no substantial or radical distinction which is indispensable to Descartes in order to conceive physic’s proper quantitative object: the matter whose essence is the extension and whose properties are geometric and mechanic, cf. [Monroy-Nasr 2002].

30 I will not go into a discussion on the interpretations of Gabbey or Martial Gueroult before him. Daniel Garber has done this and Edward Slowlik gives us convincing arguments about why he himself is inclined towards Garber’s position [Garber 1992, 298], [Slowik 2002, 58-59]. But, besides mentioning the metaphysical problem entailed in the interpretation that finds forces within matter, I wish to underline the absence of the examination of forces regarding the Cartesian study of mechanics in the debate held by all of these authors.

31 The Cartesian “Account” or Treatise on Mechanics is not even mentioned, despite it being a specialized presentation where Descartes employs the term “force” in innumerable occasions, applying it in relation to notions of action and physical movement. I find that it is very important to recognize the sense of the Cartesian “force”, “the action required to [...] produce an effect”, as an early concept of today’s physical notion of work.11 Being so, the force in Descartes’ conception does not go against the coherence between the radical dualism that he institutes and his resulting soulless physics.

Acknowledgment

32 This work has been supported by the research projects [DGAPA-PAPIIT IN401809, IN404311 and IN403012/National Autonomous University of Mexico].

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BIBLIOGRAPHY

BOUASSE, Henri [1895], Introduction à l’étude des théories de la mécanique, Paris: George Carré.

DES CHENE, Dennis [1996], Physiologia. Natural Philosophy in Late Aristotelian and Cartesian Thought, Ithaca; London: Cornell University Press.

DESCARTES, René [1963-1973], Œuvres Philosophiques, Paris: Garnier, selection presentation and notes by Ferdinand Alquié.

—— [1984], The Philosophical Writings of Descartes, vol. III, Cambridge: Cambridge University Press, translated by J. Cottingham, R. Stoothoff and D. Murdoch, Cambridge: Cambridge University Press, 1991; with A. Kenny’s correspondence anthology incorporated [CSM-K] .

GABBEY, Alan [1980], Force and inertia in the seventeenth century: Descartes and Newton, in: Descartes: Philosophy, Mathematics and Physics, edited by S. Gaukroger, Sussex: Harvester Press, 230–320.

GARBER, Daniel [1992], Descartes’ Metaphysical Physics, London; Chicago: University of Chicago Press.

GUEROULT, Martial [1980], The metaphysics and physics of force in Descartes, in: Descartes: Philosophy, Mathematics and Physics, edited by S. Gaukroger, Sussex: Harvester Press, 196–229.

HOFFMAN, Paul [2009], Essays on Descartes, Oxford: Oxford University Press.

JAMMER, Max [1957], Concepts of Force. A Study in the Foundations of Dynamics, Cambridge, MA: Harvard University Press.

MONROY NASR, Zuraya [2002], Cartesian physics and the incorporeal mind, in: Biological and Medical Sciences, edited by D. Buican & D. Thliffrey, Liege: Brepols, Collection de Travaux of the International Academy of History of Science, 59–65.

SLOWIK, Edward [2002], Cartesian Spacetime. Descartes’ Physis and the Relational Theory of Space and Motion, Dordrecht; Boston; London: Kluwer Academica Publishers.

TIPPENS, Paul [2002], Física. Conceptos y aplicaciones, Mexico: Mc Graw-Hill, 6th edn.

NOTES

1. Alquié understands this as the assertion that in the future he would only dedicate to medical studies. 2. “Expériences” is translated into English as “observational data” [CSM-K III 66]. 3. The editions of Descartes’ works used here are: Œuvres Philosophiques, edited by Ferdinand Alquié [A], following the standard notation from Adam & Tannery [AT]; The Philosophical Writings of Descartes, translated by John Cottingham, Robert Stoothoff and Dugald Murdoch [CSM]; with A. Kenny’s correspondence anthology incorporated [CSM-K] in Vol. III. 4. “A copy of the ‘Account’ was found among Descartes’ papers after his death, and a copy was published by Nicolas Poisson in 1668” [CSM-K III 66–67]. 5. Quoted by Alquié [A I 802–803]. 6. Jammer does not quote AT. He refers to Selections of R. M. Eatem, Scribner, NY 1927, xxiii. 7. In CSM the translation is: “the body is tending or striving to move in different directions [...]” [Pr III 57: CSM I 259].

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8. Descartes is referring to the normal trajectory of bodies while in motion, which is different of their always circular movement. 9. This quotation does not appear in CSM. I take the quotation from [Garber 1992, 219]. 10. [Gabbey 1980, 236-238]; cf. too [Gueroult 1980], and [Hoffman 2009]. 11. Throughout the “Account”, as Alquié points out, Descartes mentions some other forces that in fact intervene but that he has left aside, i.e., the force necessary to move the machine or in the case of the inclined plane, the force needed to move horizontally the body to be displaced. Descartes found certain differences between the trajectories traced and those rigorously demanded. Anyway, among the “other forces” neglected by Descartes, we find no indication that they may be thought inherent to matter. Perhaps, in the “Account” Descartes’ description showed what we nowadays consider the discrepancy between empirical regularities and theoretical laws. According to Alquié, Descartes asked only to take into account only the clarified principle and the conception that modern use would replace with the notion of “work”, this means “the action required to [...] produce an effect” cf. [A I 813, note 1].

ABSTRACTS

Descartes’ metaphysical dualism has important consequences for his physics. He intended to establish a certain and quantitative knowledge about the physical world, and his dualism drove away all kind of spirits or forces from it. Nevertheless, ``forces’’ do not seem completely absent in his natural philosophy. Some contemporary scholars think that Descartes, in some passages of The World and the Principles of Philosophy, expresses himself as if the forces described were ``real’’ properties of the bodies. Therefore, in this paper I will argue in favor of Cartesian dualism’s coherence, making use of a little-known notion of force proposed by Descartes.

Le dualisme métaphysique de Descartes a des conséquences importantes pour la physique qu’il a développée. Descartes cherchait à établir une connaissance quantitative et certaine du monde physique, et son dualisme en a retiré toute forme d’esprit ou de force. Néanmoins, « les forces» ne semblent pas totalement absentes de sa philosophie naturelle. Quelques auteurs contemporains estiment que Descartes, dans certains passages du Monde, et des Principes de la Philosophie, s’exprime comme si les forces décrites étaient des propriétés « réelles» des corps. Par conséquent, dans cet article, je vais donner des arguments en faveur de la cohérence du dualisme cartésien, en utilisant une notion peu connue de « force» proposée par Descartes.

AUTHOR

ZURAYA MONROY-NASR National Autonomous University of Mexico (Mexico)

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Exchanging Quantum Particles

Tomasz Bigaj

1 Introduction

1 The philosophical debate over the meaning of the notion of individuality in quantum mechanics has been raging for decades. Given that virtually all positions and arguments have been thoroughly examined and re-examined, what rationale can be offered for yet another paper on such a well-researched topic? The main goal of this article is modest: I would like to revisit the notion of a permutation of objects which is a key but somewhat neglected concept. My suggestion is that if we acknowledge the fact that there is a conceptual gap between the unique mathematical notion of a permutation and its physical realizations, we can notice that there may be more than one acceptable interpretation of the latter. This is hardly a new and surprising idea; however to my knowledge no serious attempt to classify and examine possible interpretations of physical permutations of objects has been made in the context of quantum mechanics.

2 The starting point of this article is a discussion of four possible interpretations of the notion of physical exchange, of which I select two that seem best suited for an analysis of permutation invariance in quantum mechanics: exchange of essences and exchange of haecceities. A deeper investigation of both concepts reveals that they lead to radically different conclusions regarding the problem of discernibility of quantum particles. I argue that the essentialist interpretation of exchange invalidates the standard argument in favor of the Indiscernibility Thesis given by [French & Redhead 1988]. The proof of the Indiscernibility Thesis goes through only under the alternative, haecceitist interpretation. Moreover, I claim that essentialism actually strongly suggests that identical fermions and bosons can be absolutely discerned in some states by their quantum-mechanical properties. The formal proof of this fact which I present in the article is prefaced by a discussion of how to represent the properties of individual components of many-particle systems when meaningful operators are restricted to the symmetric ones. I end the article with an appeal for further study of the essentialist view, which is a relatively new and potentially fruitful approach.

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2 Four notions of exchange

3 Formally, a permutation of an n-element set X is defined as a bijection mapping this set onto itself σ : X → X. In the context of mathematical physics the most typical permutations are those of the indices in a compound mathematical object Ψ(1, 2, …, n) (it can be a real-valued function, a vector, a density matrix, or any other object) representing a particular physical situation. Permutations applied to Ψ can be interpreted as mappings connecting it with objects arising as a result of permuting its indices: σ(Ψ(1, 2, …, n)) = Ψ(σ(1), σ(2), …, σ(n)). In the simplest case of an object containing just two indices the only non-trivial permutation leads from Ψ(1, 2) to Ψ(2, 1). The idea is of course that indices 1 and 2 are supposed to refer to physical entities (particles, properties, states of affairs, etc.), so the mathematical object Ψ(2, 1) should correspond to the situation obtained from the one described by Ψ(1, 2) by exchanging the required physical counterparts.

4 But the notion of swapping physical objects is not so clear-cut. We have to remember that mathematical concepts do not always perfectly match physical reality. Sometimes mathematical language creates artifacts (so-called surplus structures) not corresponding to anything real, and sometimes one physical situation receives many non-equivalent mathematical representations. In other cases one and the same mathematical concept can be interpreted physically in many different ways. Oftentimes failure to realize that there is no one-to-one correspondence between mathematical and physical concepts leads to serious misunderstandings.1

5 I suggest that at least four independent interpretations of the notion of exchange of physical objects can be given. The most natural way of thinking about exchanging physical objects is in terms of their location. If I asked you to swap this chair with that table, you would most probably move the chair to the place where the table stood, while simultaneously bringing the table to the location previously occupied by the chair. Hence the first interpretation presents itself naturally:

Exchange No1 (exchange of locations). To exchange an object A located in rA with an

object B located in rB is to create a situation in which in rA there is an object which

possesses all the non-relational (intrinsic) properties of B, while in rB there is an object which possesses all the non-relational properties of A.

6 The second interpretation of exchange requires an introduction of an important notion of essential properties. As is standard in the literature, I will understand the essence of an individual object as the set of properties which this object possesses in all possible worlds in which it exists. My presupposition is that all objects have essences; however, I do not assume that each essence is unique. In fact, objects in the actual world can share their essences. One important example of essential properties is what quantum physicists call “intrinsic” (or state-independent) properties of elementary particles (among state-independent properties of an electron are its mass, charge, and total spin). It is of crucial importance to acknowledge that all particles of the same type (what physicists call, confusingly, “identical” particles, such as electrons, protons, muons) have the same essence. Exchange No2 (exchange of essences). The result of an exchange of an object A,

whose essence is EA, with an object B, whose essence is EB, is a situation in which

there is an object A′ possessing properties EA and all non-essential properties of B

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(relational and non-relational), and an object B′ possessing properties EB and all non-essential properties of A. 7 If we consider for instance an electron in a particular quantum state |u⟩ and a positron in a different state |v⟩, then after their exchange-of-essences we will have a new situation in which some electron is in state |v⟩, and some positron is in state |u⟩.

8 The third interpretation requires an introduction of a new and controversial metaphysical notion. This is the notion of the haecceity of an object (also called primitive thisness). It is sometimes claimed that apart from its “ordinary” properties, essential or not, each object comes equipped with a special property, which is simply defined as being identical with itself and nothing else. Haecceity is well known to be offensive to any genuine empiricist. It cannot be characterized in a qualitative way, nor can it be directly observed or detected. And yet some philosophers feel that haecceity is necessary in order to speak about the relation of numerical distinctness and identity that is conceptually independent from qualitative identity. For now I do not wish to enter the philosophical debate on the nature and admissibility of the concept of haecceity.2 Instead, I am simply going to introduce my third concept of exchange of objects. Exchange No3 (exchange of haecceities). The result of an exchange of an object A

possessing haecceity HA with an object B possessing haecceity HB is a situation in

which an object possessing haecceity HA has all the properties (relational and non-

relational) of B, and an object possessing HB has all the properties of A. 9 It is characteristic that the process of a type 3 exchange results in a situation which is qualitatively (and hence empirically) indiscernible from the initial one, and yet we assume this situation to be ontologically different (it is supposed to be a genuinely new state of affairs). It is a scenario in which this table becomes qualitatively indistinguishable from that chair (and also assumes the location of the chair) without actually ceasing to be itself. Of course for this notion of exchange to be consistent we have to assume that objects do not possess any essential properties except their haecceities.

10 Finally, we may want to introduce an even thinner concept of exchange. In the exchange of the third type there was no epistemological difference between the initial and the final states, but an ontological one. Now we consider a case in which there is no ontological difference but a mere difference in language.

Exchange No4 (exchange of labels). An exchange of an object A which bears a label LA

with an object B which bears a label LB results in a situation in which there are objects A′ and B′ qualitatively and otherwise identical with A and B and such that A′

bears the label LB while B′ bears the label LA. 11 Given that the idea of an exchange of objects somehow involves the notion of retaining numerical identity in spite of undergoing superficial changes, we may note that each of the four introduced concepts of exchange corresponds to a slightly different intuition of what it takes for an object to remain the same entity. Exchange No1 presupposes that an object’s location is irrelevant to its identity, and that retaining all other properties is sufficient for it to be itself. Definition 2 implies that for an object to remain itself it is necessary that it should keep a particular subset of the set of its properties. According to the third notion, an object’s identity is defined by its haecceity. The fourth option seems to be based on the rather absurd idea that the identity of an object can be somehow associated with its name.

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3 Permutations in physics

12 In the next step we will address the question of which of the four available notions of exchange should be used as a physical interpretation of the mathematical notion of permutation. As a first example, let us consider the classical state of two particles at time t given by their position and velocity as follows:

r1(t) = r, v1(t) = v,

r2(t) = r′,v2(t) = v′. 13 The result of the permutation of indices is the set of the following functions:

r2(t) = r, v2(t) = v,

r1(t) = r′ ,v1(t) = v′. 14 From this it clearly follows that the corresponding physical exchange of two particles cannot be interpreted as exchange No1, since in that case the resulting functions would be

r1(t) = r′, v1(t) = v,

r2(t) = r,v2(t) = v′. 15 The idea of an exchange of position obviously does not take into account the fact that in physics position is treated as no different from any other variable characterizing a particle (velocity, momentum, angular momentum, etc.). Of the remaining three notions of a physical exchange, the exchange of labels is the least interesting because it is essentially a redescription of the same physical situation. Thus it can be claimed that there are only two interesting notions of exchange available: the exchange of essences and of haecceities.

16 The difference between the two concepts is clearly visible when we consider a permutation of two particles of different types. If we interpreted a permutation of indices in the description of the state of a positron and an electron as representing exchange of essences, then the permuted function would describe a situation in which the electron is in the state initially occupied by the positron, and vice versa. In contrast, the exchange of haecceities leads to the state in which the object possessing the haecceity of the electron now has all the properties (state-dependent and state- independent) of the positron, and likewise for the positron. Thus the permuted and non-permuted functions describe ontologically distinct states which are nevertheless empirically indistinguishable.

17 Let us now apply our selected interpretations of physical exchange to the analysis of the fundamental symmetrization/antisymmetrization postulate of quantum mechanics. The textbook way to introduce this postulate is through the concept of exchange degeneracy.3 Considering the joint state of two particles of the same type such that one of them occupies state |u⟩ whereas the other one is in a different state |v⟩, we

should observe that the two permuted states |u⟩1|v⟩2 and | v⟩1|u⟩2 are empirically indistinguishable. According to the essentialist approach this indistinguishability comes from the fact that both bi-partite states represent one and the same physical state of affairs. On the other hand, the haecceitist approach admits that there is a difference between the permuted and non-permuted states, but this difference cannot give rise to any observational effects, as haecceities are not empirically accessible.

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18 In order to avoid the degeneracy problem, we adopt the symmetrization postulate, which narrows down the admissible states to the symmetric (occupied by bosons) and antisymmetric ones (applicable to fermions). Thus the only vector that can properly represent the above-discussed state of two electrons is the antisymmetric superposition

19 In the case of bosons, the state has to be symmetric

20 Given that in the quantum-mechanical formalism the sign of a vector has no physical meaning, it is commonly accepted that both types of vectors display the required permutation invariance which follows from the indistinguishability postulate regarding particles of the same type.

4 The Indiscernibility Thesis (IT)

21 The standard view is that this permutation invariance has dramatic consequences regarding the ontological status of quantum particles of the same type. Most famously, it is argued that fermions and bosons of the same type are indiscernible by their properties and relations, and hence they violate the Principle of the Identity of Indiscernibles (PII). Recent foundational work on the notion of discernibility has revealed that there are many non-equivalent ways of interpreting this concept,4 so we have to be precise about what particular type of discernibility is claimed to be violated by quantum particles. The logically strongest grade of discernibility is known as absolute discernibility, and it can be roughly defined as follows: two objects a and b are absolutely discernible iff there is an open formula in one variable consisting of predicates representing admissible properties or relations which is satisfied by a but not by b. The Indiscernibility Thesis applied to quantum particles of the same type can be formulated as the negation of their absolute discernibility: (IT) Distinct fermions (bosons) of the same type are never absolutely discernible by their properties or relations.

22 Although suggestions that quantum particles may violate PII were made quite early on in the history of quantum mechanics, the first rigorous proof of this fact was given in [French & Redhead 1988] and was subsequently generalized and improved upon in other publications.5 French & Redhead’s proof is based on the assumption that when we consider a set of n particles of the same type, any property of the ith particle can be (1) (2) (i) (n) represented by an operator of the form Oi = I ⊗ I ⊗ … ⊗ O ⊗ … ⊗ I , where O is a Hermitian operator acting on the single-particle Hilbert space ℋ. Now it is easy to prove

that the expectation values of two such operators Oi and Oj calculated for symmetric and antisymmetric states are identical. Similarly, it can be proved that the probabilities of revealing any value of observables of the above type conditional upon any measurement outcome previously revealed are the same for all n particles.

23 In what follows I will argue that the Indiscernibility Thesis is actually contingent upon the selection of one of the two available interpretations of exchange of particles that we have discussed in the previous section. More specifically, I will try to show that the

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argument in favour of IT goes through only if we accept the exchange of haecceities interpretation. However, under the alternative essentialist interpretation, it can actually be argued that fermions and bosons are absolutely discernible in certain typical configurations.

24 My first argument is based on the observation that the exchange-of-essences interpretation leads to the symmetrization postulate regarding admissible observables, which effectively excludes non-symmetric observables used by French & Redhead in their proof of IT. To see that this is the case, let us recall that if we interpret the

permutation P12 as exchanging essences of particles 1 and 2, the mathematical vectors |

ψ⟩ and P12|ψ⟩ actually represent one and the same physical state (under the condition that |ψ⟩ describes a state of two indistinguishable particles having the same essences). Hence no physically meaningful observable can discriminate between the two permuted vectors. To put it more precisely, the only admissible operators are those

whose expectation values are identical in “both” states |ψ⟩ and P12|ψ⟩ : ⟨ψ|O|ψ⟩ = ⟨ψ|

P12OP12|ψ⟩. But of course this equation must hold regardless of the choice of the state |ψ

⟩, and this means that the operator O commutes with the permutation operator P12. Yet

clearly the operators Oi introduced by French & Redhead do not commute with

permutation operators, as can be seen in the following commutation relation: PijOiPij =

Oj. 25 French & Redhead are aware of the problem . Their response to it is based on the distinction between observable and unobservable properties. But I believe that this reply has no force in the context of the exchange-of-essences interpretation. The

permuted states |ψ⟩ and P12|ψ⟩ are not merely observationally indistinguishable—they are metaphysically identical. An operator which “sees” a difference between numerically identical physical states merely because of their (or rather “its”) different mathematical representations cannot possibly represent any physically meaningful property, whether observable or not.

26 In my mind French & Redhead’s response makes sense only under the alternative

haecceity interpretation. Here the vectors |ψ⟩ and P12|ψ⟩ represent observationally indistinguishable but numerically distinct states of affairs. Thus, it can be claimed that

operators Oi and Oj, whose expectation values in states |ψ⟩ and P12|ψ⟩ are different, represent some “hidden” properties of the entire system, reflecting the ontological

distinctness between the permuted states. Speaking loosely, each operator Oi is “attached” to a different haecceity via its label i, so when we swap haecceities between

particles i and j, clearly the result should be “registered” by Oi. But no physically meaningful operator can register any difference between a situation and itself, regardless of how we decide to represent it mathematically.6

5 Essentialism and discernibility

27 But this is not the end of the story. The fact that one particular argument in favor of IT turns out to be incorrect does not show that the thesis itself is false. We need a direct proof that the exchange-of-essences interpretation leads to the conclusion that some particles of the same type are indeed absolutely discernible. Finding just one physical property such that only one particle occupying a joint symmetric/antisymmetric state possesses it is all we need to reach our goal. But before we can do that, we must address

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the question of how to properly represent measurable characteristics of individual particles when the admissible operators are restricted to symmetric ones.

28 Let us consider any one-dimensional projection operator P acting on a single-particle Hilbert space. As is well-known, such an operator is taken to represent a specific quantum-mechanical property of an individual particle. Moreover, using the whole family of such projection operators we can in principle describe any physical property of a particle. But our goal now is to construct a new projector acting on the tensor product of two Hilbert spaces which could represent the statement that (at least) one of two indistinguishable particles possesses property P. It is relatively straightforward to notice that such an operator Ω should satisfy the following desiderata: 1. Ω should be Hermitian, 2. Ω should be symmetric, 3. Ω should be a projector (and therefore idempotent), 4. Ω should be the sum of tensor products of one-particle operators involving only P and I (the identity).

29 From conditions (2) and (4) it follows that the most general form Ω can have is the following: Ω = aP ⊗ I + aI ⊗ P + bP ⊗ P. 30 Given that Ω is assumed to be Hermitian, coefficients a and b have to be real. Now we can apply requirement (3): Ω2 = Ω.

31 Let us calculate the square of Ω (using the fact that P2 = P): Ω2 = a2P ⊗ I + a2I ⊗ P + (2a2 + 4ab + b2)P ⊗ P. 32 Comparing formulas for Ω and Ω2 we can first derive a2 = a. This equation obviously has two solutions in real numbers (0 and 1), but we can discard the value 0, as the operator P ⊗ P clearly represents the situation in which both particles have the same property. If we put a = 1, we can easily solve the quadratic equation in b which arises as the result of equating the coefficients of the component P ⊗ P in the expansions of Ω and Ω2. Thus the only two solutions are as follows:

Ω1 = P ⊗ I + I ⊗ P − P ⊗ P,

Ω2 = P ⊗ I + I ⊗ P − 2P ⊗ P.

33 However, we don’t have to make a choice between Ω1 and Ω 2 in order to prove the

following theorem. It is not difficult to observe that Ω1 represents the question “Does at

least one particle possess property P?” while Ω2 the question “Is it true that one particle possesses property P while the other does not possess P?” See an extensive analysis given in , . Theorem 1. ‎ Let Ψ be a normalized vector a|u⟩1|v⟩2 + b|v⟩1|u⟩2 where |u⟩ and |v⟩ are mutually orthogonal unit vectors, and let P = |u⟩⟨u|. Then the expectation value of

both operators Ω1 and Ω2 in state Ψ is 1. 34 Here is a sketch of the calculation confirming this fact: ⟨Ψ|P ⊗ I|Ψ⟩ = ⟨a * uv + b * vu|P ⊗ I|auv + bvu⟩ = a * a⟨u|P|u⟩ + b * b⟨v|P|v⟩ = |a|2. 35 Analogously, it can be showed that ⟨Ψ|I ⊗ P|Ψ⟩ = |b|2. 36 And because the expectation value of P ⊗ P in Ψ vanishes due to the orthogonality relation between |u⟩ and |v⟩, we finally arrive at the sought-after result: 2 2 ⟨Ψ|Ω1|Ψ⟩ = ⟨Ψ|Ω2|Ψ⟩ = |a| + |b| = 1

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37 What is the meaning of this formal derivation? It can be unpacked as follows: given the only available mathematical representation of the statement “At least one particle possesses property P”, if the system is prepared in a superposition of the product of two

orthogonal states |u⟩1|v⟩2 and its permuted form |v⟩1|u⟩2, at least one of the two particles possesses the property associated with state |u⟩. But exactly the same can be proved with respect to the state |v⟩. Consequently, we have to admit that at least one particle has the property associated with |u⟩, and at least one particle has the property associated with |v⟩. But clearly one particle cannot be both in state |u⟩ and state |v⟩. Thus we have proved that the particles prepared in state Ψ are discernible by their properties P = |u⟩⟨u| and Q = |v⟩⟨v|. This result obviously applies to bosons and fermions, as symmetric and antisymmetric states are just special cases of the superposition Ψ.

38 It may be instructive to see why this conclusion is avoidable under the alternative, haecceistic interpretation of permutation. Of course, the formal result of Theorem 1 still stands, as it is a mathematical fact, but its physical interpretation changes. Haecceitism implies that there is a meaningful difference between labels, as they refer to numerically distinct entities with different primitive identities. Consequently, we can conceptually (although not observationally) distinguish between statements “Particle 1 has property P” and “Particle 2 has property P”. The first statement is deemed true if and only if the operator P ⊗ I receives expectation value 1 in state Ψ, whereas the second one corresponds to the operator I ⊗ P and its expectation value. For the haecceitist the correct interpretation of the statement “At least one particle possesses property P” is just the classical disjunction of the above-mentioned individual statements: “Particle 1 has property P or particle 2 has property P”. And in the case in which none of the disjuncts receives the value “true” the entire disjunction cannot be true.

39 The haecceitist interprets the fact that the operator Ω1 has its expectation value equal 1 in Ψ as a mere indication of the fact that when we decide to measure P on both particles, one measurement will reveal value 1 with certainty. But this doesn’t mean that any particle possesses the corresponding property P before the measurement. So Ω

1 can be construed as referring to whatever property of the entire system is responsible for the predicted behavior (most likely this property has a fundamental dispositional character). But I would like to stress that without the “thick” metaphysics of primitive identities the disjunctive interpretation of the statement “At least one particle has property P” would not be available. Without haecceities we have only two options:

either to accept Ω1 as a formal representation of this property, or to admit that the property in question is not expressible at all in our impoverished symmetric language.

6 Conclusion

40 I have laid down two main philosophical positions regarding the meaning of permutation invariance in quantum mechanics: the essentialist view and the haecceitistic view. I have argued that both views come in whole packages, including a lot more than the mere philosophical interpretations of the notion of permutation. Essentialism leads to the strong symmetrization postulate with respect to admissible observables, which prevents us from representing properties of individual particles

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with the help of non-symmetric, label-bearing operators. Generally, essentialism repudiates the use of labels (indices) as names with fixed reference, and instead treats them only as formal devices enabling us to consider certain mathematical symmetries. Finally, it can be argued that insofar as essentialism is capable of formulating and solving the problem of absolute discernibility of particles of the same type at all, its answer is that both fermions and bosons can be actually discerned by their properties.

41 On the other side of the divide, haecceitism has to make the distinction between physically meaningful Hermitian operators and operators corresponding to observable properties. Operators which represent properties of individual particles are meaningful but, strangely enough, they are not literally observables. Labels used in the formal description of many-particle states are to be treated literally: they follow the primitive identity of individual objects. The Indiscernibility Thesis follows under this view from the fact that the expectation values for all single-particle operators are the same in antisymmetric/symmetric states. One surprising feature of haecceitism is that it is actually a necessary component of IT. Without haecceitism the argument for the indiscernibility claim could not even get off the ground.7

42 Due to the lack of space I can’t discuss in detail what I consider the greatest challenge to the essentialist interpretation and the associated claim that absolute discernibility is attainable for quantum particles of the same type. This challenge is a consequence of the fact that in the state resulting from the antisymmetrization of the product state |u⟩

1|v⟩2 there are infinitely many projectors representing single-particle properties other than |u⟩ and |v⟩ whose expectation values equal 1. As a result, it seems that we would have to admit that individual particles possess mutually incompatible properties. This problem requires an extensive and thorough evaluation which has to be saved for another occasion.

43 I would like to end this survey with a plea on behalf of essentialism. The fact that the essentialist approach admits the possibility of discerning quantum particles by their properties fits well the everyday practice of experimental physicists who have no qualms about talking of the electron in a bubble chamber as being an entity different from an electron in the Andromeda galaxy. Although essentialism entails that in some cases quantum particles may occupy states which render them indiscernible, this does not necessarily rob them of the status of individuals, if we follow Dieks & Versteegh and define individuals as objects for which it is possible to be in a state in which they possess different properties [Dieks & Versteegh 2008]. I am aware of the conceptual difficulties afflicting this position, and I admit that at this point I can’t offer a satisfactory solution to all of them. But I believe that the advantages of the essentialist interpretation merit further investigation into this new approach to the problem of identity and individuality in quantum mechanics.

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BUTTERFIELD, Jeremy [1993], Interpretation and identity in quantum theory, Studies in History and Philosophy of Science – Part A, 24(3), 443–476, doi:10.1016/0039-3681(93)90037-K.

COHEN-TANNOUDJI, Claude, DIU, Bernard, & LALOË, Franck [1977], Quantum Mechanics, New York: Wiley.

DIEKS, Dennis & VERSTEEGH, Marijn A. M. [2008], Identical quantum particles and weak discernibility, Foundations of Physics, 38(10), 923–934, doi:10.1007/s10701-008-9243-z.

FRENCH, Steven [2011], Identity and individuality in quantum theory, in: The Stanford Encyclopedia of Philosophy, summer 2011 edn., URL http://plato.stanford.edu/archives/sum2011/entries/qt- idind/.

FRENCH, Steven & KRAUSE, Decio [2006], Identity and Physics: A Historical, Philosophical and Formal Analysis, Oxford: Clarendon Press.

FRENCH, Steven & REDHEAD, Michael [1988], Quantum physics and the identity of indiscernibles, The British Journal for the Philosophy of Science, 39(2), 233–246, doi:10.1093/bjps/39.2.233.

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GHIRARDI, GianCarlo, MARINATTO, Luca, & WEBER, Tullio [2002], Entanglement and properties of composite quantum systems: A conceptual and mathematical analysis, Journal of Statistical Physics, 108(1–2), 49–122, doi:10.1023/A:1015439502289.

HAWLEY, Katherine [2006], Weak discernibility, Analysis, 66(4), 300–303, doi:10.1093/analys/ 66.4.300.

HUGGETT, Nicholas [2003], Quarticles and the identity of indiscernibles, in: Symmetries in Physics, edited by W. K. Brading & E. Castellani, Cambridge: Cambridge University Press, 239–249.

LADYMAN, James & BIGAJ, Tomasz [2010], The principle of the identity of indiscernibles and quantum mechanics, Philosophy of Science, 77, 117–136.

LADYMAN, James, LINNEBO, Øystein, & PETTIGREW, Richard [2012], Identity and discernibility in philosophy and logic, The Review of Symbolic Logic, 5, 162–186, doi:10.1017/S1755020311000281.

MAUDLIN, Tim [1988], The essence of space-time, in: Proceedings of the Biennial Meeting of the Philosophy of Science Association, edited by A. Fine & J. Leplin, East Lansing: Philosophy of Science Association, vol. 2, 82–91.

MULLER, Fred A. & SAUNDERS, Simon [2008], Discerning fermions, The British Journal for the Philosophy of Science, 59(3), 499–548, doi:10.1093/bjps/axn027.

MULLER, Fred A. & SEEVINCK, M. P. [2009], Discerning elementary particles, Philosophy of Science, 76, 179–200.

SAUNDERS, Simon [2006], Are quantum particles objects?, Analysis, 66(289), 52–63, doi:10.1111/j. 1467-8284.2006.00589.x.

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TELLER, Paul [1995], An Interpretive Introduction to Quantum Field Theory, Princeton: Princeton University Press.

VAN FRAASSEN, Bas C. [1991], Quantum Mechanics: An Empiricist View, Oxford: Clarendon Press.

VAN FRAASSEN, Bas C. & PESCHARD, Isabelle [2008], Identity over time: objectively, subjectively, The Philosophical Quarterly, 58(230), 15–35, doi:10.1111/j.1467-9213.2007.533.x.

NOTES

1. Tim Maudlin makes a similar observation in the context of the debate on the ontological status of space-time [Maudlin 1988, 83ff.]. He points out that the fact that a diffeomorphism transforms one mathematical representation of space-time into a distinct representation does not imply that the corresponding physical realizations have to be different. Maudlin addresses a question very similar to the one we consider here: what is the best physical interpretation of the mathematical notion of a diffeomorphism connecting individual mathematical points? And his solution is closely related to the essentialist interpretation of permutation that I present later in this section. 2. An excellent philosophical discussion of the notion of haecceity in the context of quantum mechanics can be found in [Teller 1995, 16–35]. 3. For an extended discussion, see e.g., [Cohen-Tannoudji, Diu et al. 1977, 1370–1408]. 4. See for instance a comprehensive logical analysis of various grades of discernibility in [Ladyman, Linnebo et al. 2012] and [Bigaj 2014]. Simon Saunders noticed that the notion of discernibility figuring in the usual formulation of PII admits different logical reconstructions. Saunders rediscovered the distinction made by Quine between absolute, relative and weak grades of discernibility, and suggested that quantum particles are indeed weakly discernible. This claim was subsequently accepted and refined in [Saunders 2006], [Muller & Saunders 2008], [Muller & Seevinck 2009]. Criticism of the weak discernibility thesis can be found, e.g., in [Hawley 2006], [Dieks & Versteegh 2008], [van Fraassen & Peschard 2008], [Ladyman & Bigaj 2010]. 5. The list of publications analyzing the violation of PII in quantum mechanics is long, and it contains, among others, [van Fraassen 1991], [Butterfield 1993], [Huggett 2003], [French & Krause 2006]. IT is so commonly accepted in the literature that it could be referred to as the Received View, if not for the fact that Steven French has already appropriated this term to speak about a different position which questions the individuality of quantum particles of the same type, see e.g., [French 2011]. 6. Nick Huggett generalizes French & Redhead’s proof of IT in a way which may seem to threaten my argument [Huggett 2003]. He shows that we don’t actually need to assume that observables Oi have the specific non-symmetric form required by French & Redhead. Huggett’s proof of the fact that Oi and Oj have the same expectation values in symmetric (antisymmetric) states relies on two assumptions only: the commutation relation PijOiPij = Oj (which he calls the conjugacy condition), and the independence condition PijOkPij = Ok (for k ≠ i and j). However, I’d like to point out that if we assume (as is required under the essentialist view) that operators Oi are symmetric, the conjugacy condition immediately implies that Oi = Oj for all i and j. It is hardly an exciting theorem that identical operators have the same expectation values in all states. 7. This point, as I believe, must have somehow escaped the notice of main experts in the field. For instance, French & Krause famously defend their thesis of the underdetermination of metaphysics by physics by pointing out that the quantum-mechanical description of systems of many particles can support two different metaphysical views: one stating that particles are individuals distinguished by their unique haecceities, and the other that they are non-individuals [French & Krause 2006, 189–197]. But if quantum particles are non-individuals which cannot be

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meaningfully referred to with the help of different labels, then as I noticed the standard argument in favor of the Indiscernibility Thesis cannot even be formulated. On the other hand, it may seem that the essentialist interpretation of exchange will be more sympathetic to the “particles as non-individuals” view. But this suggestion flies in the face of the fact proved above that under this interpretation particles can be discerned by their qualitative properties. Thus it looks like the non-individual view is excluded by both interpretations of exchange considered in this article. One possibility of making room for this position is to argue that under the non- individual view the notion of an exchange of particles is meaningless, and as such does not require any physical interpretation whatsoever.

ABSTRACTS

The mathematical notion of a permutation of indices in the state description admits different physical interpretations. Two main interpretations analyzed in this paper are: exchange of essences and exchange of haecceities. It is argued that adopting the essentialist approach leads to the conclusion, contrary to the conventional wisdom, that quantum particles of the same type are sometimes discernible by their properties. The indiscernibility thesis can be supported only by the alternative interpretation in terms of primitive thisness.

La notion mathématique de permutation d'indices dans la description de l'état peut recevoir différentes interprétations physiques. Deux interprétations principales analysées dans cet article sont l'échange des essences et l'échange des heccéités. On soutient ici qu'adopter l'approche essentialiste conduit à la conclusion selon laquelle les particules quantiques d'un même type sont parfois discernables par leurs propriétés, conclusion contraire à la sagesse conventionnelle. Seule l'interprétation alternative de l'heccéité primitive permet de soutenir la thèse de l'indiscernabilité.

AUTHOR

TOMASZ BIGAJ University of California, San Diego (USA) University of Warsaw (Poland)

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Truth as Contextual Correspondence in Quantum Mechanics

Vassilios Karakostas

This work has been supported by the research programme “Thalis” co-financed by the European Union (ESF) and the Hellenic Research Council (project 70-3-11604).

1 Introduction

1 In investigations concerning the problem of truth in the physical sciences, the correspondence theory of truth has frequently been thought of as the most eminent. Although the correspondence theory admits various different formulations, the core of any correspondence theory is the idea that a proposition is true if and only if it corresponds to or matches reality. The classicalversion of the theory describes this relationship as a correspondence to the facts about the world, e.g., [Burgess & Burgess 2011, 70–72]. If so, then adopting a correspondence theory of truth amounts to endorsing instances of the following scheme: [CF] The proposition that P is true if and only if P corresponds to a fact.

2 Alternatively, if one construes the notion of a “fact” in terms of the weaker notion of an obtaining “state of affairs”, as in an Austin-type theory, then, [CF] is re-expressed as follows: [CS] The proposition that P is true if and only if there is a state of affairs X such that P corresponds to X and X obtains.

3 The useful feature of states of affairs is that they refer to something that can be said to obtain or fail to obtain, to be the case or not to be the case, to be a fact or fail to be a fact, that is, they exist even when they are not concretely manifested or realized.

4 Regardless of the exact formulation of a correspondence account of truth, correspondence theorists normally conceive of truth as a non-epistemic notion; that is, a proposition cannot be claimed true or false in virtue of its knowability or provability,

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e.g., [Devitt 2001, 606]. Any proposition is either determinately true or determinately false independently of our power to establish which value it is. Even if it is impossible to produce a basis on which we may ascertain the truth value of a proposition this does not imply that it does not possess any such value. It always has one. The possession of truth values is therefore entirely independent of our means of warranting their assignment. In this sense, the truth of a proposition is also supposed to transcend our possible knowledge of it, or its verification. I shall argue immediately below that the propositional structure of classical mechanics allows truth-value assignments in conformity with such a traditional conception of a correspondence account of truth.1

2 Truth-value assignment in classical mechanics

In classical mechanics a system S with n degrees of freedom is described by a phase

space ΩS with 2n coordinates {qi, pi} which correspond to generalized position and momentum coordinates. The state of S at any temporal moment t is represented by a

point Xt = {qi(t), pi(t)} of ΩS. Physical quantities are represented by real-valued functions 3 on the phase space, e.g., the position q of a mass point is a function q : ΩS → R . Physical properties—namely, values of various physical quantities of the system—are

represented by Borel subspaces , , … of ΩS and will be denoted by P(A), P(B), …,

respectively. Hence, a property is represented by a characteristic function P(A) : ΩS → {0, 1} with P(A)(X) = 1 if X ∈ and P(A)(X) = 0 if X ∉ . We say that the characteristic function takes the value 1 or the property P(A) pertains to system S at

time t if the state of S is represented by a point lying in the corresponding subset (Xt ∈ ), and that P(A) does not pertain to S if the state of the system is represented by a

point outside this subset (Xt ∉ ). In terms of propositions PA, PB, … this means that a

proposition PA is true if the property P(A) pertains to S, and false otherwise. That is, the

proposition PA asserting that “system S acquires the property P(A)”, or equivalently, that “the value a of some physical quantity A of S lies in a certain range of values Δ” (“a ∈ Δ”), is true if and only if the associated property P(A) obtains. In the propositional structure of classical mechanics, each point in phase space, representing a classical state of a given system S, defines a truth-value assignment to the subsets representing the propositions. Each subset to which the point belongs represents a true proposition or a property that is instantiated by the system. Likewise, each subset to which the point does not belong represents a false proposition or a property that is not instantiated by the system. Thus, every possible property of S is selected as either occurring or not; equivalently, every corresponding proposition pertaining to S is either true or false.

5 Hence, for present purposes, the really essential thing about the mode of representation of classical systems is that the algebra of properties or propositions of a classical mechanical system is isomorphic to the lattice of subsets of phase space, a

Boolean lattice, LB, that can be interpreted semantically by a 2-valued truth function.

This means that to every proposition P ∈ LB one of the two possible truth values 1 (true) and 0 (false) can be assigned through the associated characteristic function; equivalently, any proposition is either true or false (tertium non datur), e.g., [Dalla Chiara, Giuntini et al. 2004, 21]. Thus, the propositions of a classical system are semantically decidable. They are either determinately true or determinately false independently of any perceptual evidence or cognitive means by which we may verify

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or falsify them. Classical mechanical propositions are endowed with a determinate truth value.

6 From a physical point of view this is immediately linked to the fact that classical physics views objects-systems as bearers of determinate properties. Specifically, classical physical systems are taken to obey a so-called “possessed values” or “definite values” principle that may be succinctly formulated as follows:2 Definite values principle: Any classical system is characterized, at each instant of time, by definite values for all physical quantities pertaining to the system in question.

7 That is, classical properties (values of physical quantities) are considered as being intrinsic to the system, as being possessed by the system itself. They are independent of whether or not any measurement is attempted on them and their definite values are independent of one another as far as measurement is concerned. Successive measurements of physical quantities, like position and momentum that define the state of a classical system, can be performed to any degree of accuracy and the results combined can completely determine the state of the system before and after the measurement interaction, since its effect, if not eliminable, takes place continuously in the system’s phase space and is therefore predictable in principle. Hence, during the act of measurement a classical system conserves its identity; measurement does not induce any qualitative changes on the state of the measured system. The process of measurement in classical physics is passive; it simply reveals a fact which has already occurred. Thus, the principle of value-definiteness implicitly incorporates the following assumption of non-contextuality: Non-contextuality: If a classical system possesses a property (value of a physical quantity), then it does so independently of any measurement context, i.e., independently of how that value is eventually measured.

8 This means that the properties possessed by a classical system depend in no way on the relations obtaining between it and a possible experimental or measurement context used to bring these properties about. If a classical system possesses a given property, it does so independently of possessing other values pertaining to other experimental arrangements. All properties pertaining to a classical system are simultaneously determinate, regardless of our means of exploring and warranting their assignment. Accordingly, the propositions of a classical system are considered as possessing determinate truth values—they are either determinately true or determinately false— prior to and independent of any actual investigation of the states of affairs the propositions denote; that is, classical mechanical propositions possess investigation- independent truth values, thus capturing the radically non-epistemic character of a traditional correspondence account of truth. Consequently, the propositions of a classical system are considered as being either true or false in virtue of a stable and well-defined reality which serves as the implicit referent of every proposition. All propositions are therefore meant to have determinate truth conditions, so that it does no harm to avoid specifying the exact domain of reference. Thus, in a classical universe of discourse, it is supposed to exist implicitly an Archimedean standpoint from which the totality of facts may be logically evaluated.

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3 Truth-value assignment in quantum mechanics

9 On the standard (Dirac-von Neumann) codification of quantum theory, the elementary propositions pertaining to a quantum mechanical system form a non-Boolean lattice,

LH, isomorphic to the lattice of closed linear subspaces or corresponding projection operators of a Hilbert space. Thus, a proposition pertaining to a quantum system is represented by a projection operator P on the system’s Hilbert space H or, equivalently,

it is represented by the linear subspace HP of H upon which the projection operator P projects. Since each projection operator P on H acquires two eigenvalues 1 and 0, where the value 1 can be read as “true” and 0 as “false”, the proposition “a system S in state |ψ ⟩ has the property P(A)” is said to be true if and only if the corresponding projection

operator PA obtains the value 1, that is, if and only if PA|ψ⟩ = |ψ⟩. Accordingly, the state |

ψ⟩ of the system lies in the associated subspace HA which is the range of the operator

PA, i.e., |ψ⟩ ∈ HA. In such a circumstance, the property P(A) pertains to the quantum

system S. Otherwise, if PA|ψ⟩ = 0 and, hence, |ψ⟩ ∈ ⊥ HA (subspace completely

orthogonal to HA), the counter property ¬P(A) pertains to S, and the proposition is said to be false. It might appear, therefore, that propositions of this kind have a well- defined truth value in a sense analogous to the truth-value assignment in classical mechanics.

10 There is, however, a significant difference between the two situations. Unlike the case in classical mechanics, for a given quantum system, the propositions represented by projection operators or Hilbert space subspaces are not partitioned into two mutually exclusive and collectively exhaustive sets representing either true or false propositions. As already pointed out, only propositions represented by subspaces that contain the system’s state are assigned the value “true” (propositions assigned probability 1 by |ψ⟩), and only propositions represented by spaces orthogonal to the state are assigned the value “false” (propositions assigned probability 0 by |ψ⟩) [Dirac 1958, 46–47], [von Neumann 1955, 213–217]. Hence, propositions represented by subspaces that are at some non-zero or non-orthogonal angle to the unit vector |ψ⟩ or, more appropriately, to the ray representing the quantum state are not assigned any truth value in |ψ⟩. These propositions are neither true nor false; they are assigned by |ψ ⟩ a probability value different from 1 and 0; thus, they are undecidable or indeterminate for the system in state |ψ⟩ and the corresponding properties are taken as indefinite. This kind of semantic indeterminacy imposes an inherent ambiguity with respect to the classical binary true/false value assignments, rigorously expressed, for the first time, by Kochen-Specker’s theorem. According to this, for any quantum system associated to a Hilbert space of dimension higher than two, there does not exist a 2-valued, truth-

functional assignment h : LH → {0, 1} on the set of closed linear subspaces, LH, interpretable as quantum mechanical propositions, preserving the lattice operations and the orthocomplement. In other words, the gist of the theorem, when interpreted semantically, asserts the impossibility of assigning definite truth values to all propositions pertaining to a physical system at any one time, for any of its quantum states, without generating a contradiction. What are, therefore, the maximal sets of

subspaces of LH or the maximal subsets of propositions that can be taken as simultaneously determinate, that is, as being assigned determinate (but perhaps unknown) truth values in an overall consistent manner?

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3.1 Maximal sets of simultaneously determinate propositions

11 In this respect, we employ the Bub-Clifton so-called “uniqueness theorem” [Bub 2009], [Bub & Clifton 1996]. Consider, to this end, a quantum system S represented by an n- dimensional Hilbert space whose state is represented by a ray or one-dimensional projection operator D = |ψ⟩⟨ψ| spanned by the unit vector |ψ⟩ on H. Let A be an ⊥ observable of S with m ≤ n distinct eigenspaces Ai, while the rays DAi = (D ∨ Ai ) ∧ Ai, i = 1, …, k ≤ m, denote the non-zero projections of the state D onto these eigenspaces. Then, according to the Bub-Clifton theorem, the unique maximal sublattice of the

lattice of projection operators or subspaces, LH, representing the propositions that can be determinately true or false of the system S, is given by

⊥ LH({DAi}) = {P ∈ LH : DAi ≤ P or DAi ≤ P , ∀i, i = 1, …, k}.

12 The sublattice LH({DAi}) ⊂ LH is generated by (i) the rays DAi, the non-zero projections of

D onto the k eigenspaces of A, and (ii) all the rays in the subspace (DA1 ∨ DA2 ∨ … ∨ DAk) ⊥ ⊥ = ( ∨ DAi) orthogonal to the subspace spanned by the DAi, for i = 1, …, k. The set of

maximal (non-degenerate) observables associated with LH({DAk}) includes any maximal

observable with k eigenvectors in the directions DAi, i = 1, …, k. The set of non-maximal observables includes any non-maximal observable that is a functionof one of these maximal observables. Thus, all the observables whose eigenspaces are spanned by rays

in LH({DAk}) are determinate, given the system’s state D and A.

13 Identifying such maximal determinate sets of observables amounts, in effect, to a

consistent assignment of truth values to the associated propositions in LH({DAk}) of LH,

not to all propositions in LH. LH({DAk}) represents the maximal subsets of propositions pertaining to a quantum system that can be taken as having simultaneously determinate truth values, where a truth-value assignment is defined by a 2-valued (or

Boolean) homomorphism, h : LH({DAk}) → {0, 1}. If the system’s Hilbert space H is more

than 2-dimensional, there are exactly k 2-valued homomorphisms on LH({DAk}), where th the i homomorphism assigns to proposition DAi the value 1 (i.e., true) and the

remaining propositions in LH({DAi}), i = 1, … k, the value 0 (i.e., false). The determinate

sublattice LH({DAk}) is maximal, in the sense that, if we add anything to it, lattice closure

generates the lattice LH of all subspaces of H, and there are no 2-valued

homomorphisms on LH [Bub 2009].

14 In fact, the Bub-Clifton determinate sublattice LH({DAi}) constitutes a generalization of the usual Dirac-von Neumann codification of quantum mechanics. On this standard position, an observable has a determinate value if and only if the state D of the system is an eigenstate of the observable. Equivalently, the propositions that are determinately true or false of a system are the propositions represented by subspaces that either include the ray denoting the state D of the system, or are orthogonal to D. Thus, the Dirac-von Neumann determinate sublattice can be formulated as ⊥ LH(D) = {P ∈ LH : D ≤ P or D ≤ P }. 15 It is simply generated by the state D and all the rays in the subspace orthogonal to D. If the system’s Hilbert space H is more than 2-dimensional, there is one and only one 2-

valued homomorphism on LH(D): the homomorphism induced by mapping the state D

onto 1 and every other ray orthogonal to D onto 0. Apparently, the sublattice LH(D) for a particular choice of an observable A in state D forms a subset of Bub-Clifton’s proposal

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LH({DAi}). The latter will only agree with LH(D) if D is an eigenstate of A, for then the set

{DAi} consists of only D itself. In general, the sublattice LH({DAi}) contains all the

propositions in LH(D) that it makes sense to talk about consistently with A-propositions, namely propositions that are strictly correlated to the spectral projections of some suitable preferred observable A. From this perspective, the Dirac-von Neumann sublattice is obtained by taking A as the unit (or identity) observable I. As [Bub & Clifton 1996] rightly observe, however, there is nothing in the mathematical structure of Hilbert space quantum mechanics that necessitates the selection of the preferred determinate observable A as the unit observable I, whilst, in addition, this choice leads to von Neumann’s account of quantum measurement resulting in a sequential regress ofobserving observers.

16 Then, the following question arises. What specifies the choice of a particular preferred observable A as determinate if A ≠ I? The Bub-Clifton proposal allows, in effect, different choices for A corresponding to various different “no collapse” interpretations of quantum mechanics, as for instance Bohm’s hidden variable theory, if the privileged observable A is fixed as position in configuration space, or modal interpretations that exploit the bi-orthogonal decomposition theorem, e.g., [Dieks 1989]. In them the preferred determinate observable is not always fixed but varies with the quantum state.

4 Context-dependence of truth valuation in quantum mechanics

17 In our view, if one wishes to stay within the framework of Hilbert space quantum mechanics and refrains from introducing additional structural elements, the most natural and immediate choice of a suitable preferred observable, especially, for confronting the problem of truth-value assignments, results in the determinateness of the observable to be measured. This is physically motivated by the fact that in the quantum domain one cannot assign, in a consistent manner, definite sharp values to all quantum mechanical observables pertaining to a microphysical object, in particular to pairs of incompatible observables, independently of the measurement context actually specified. In terms of the structural component of quantum theory, this is due to functional relationship constraints that govern the algebra of quantum mechanical observables, as revealed by the Kochen-Specker theorem alluded to above and its recent investigations, e.g., [Cabello 2006], [Kirchmair, Zähringer et al. 2009]. In view of them, it is not possible, not even in principle, to assign to a quantum system definite non-contextual properties corresponding to all possible measurements. This means that it is not possible to assign a definite unique truth value to every single yes-no proposition, represented by a projection operator, independent of which subset of mutually commuting projection operators one may consider it to be a member. Hence, by means of a generalized example, if A, B and E denote observables of the same quantum system, so that the corresponding projection operator A commutes with operators B and E ([A, B] = 0 = [A, E]), not however the operators B and E with each other ([B, E] ≠ 0), then the result of a measurement of A depends on whether the system had previously been subjected to a measurement of the observable B or a measurement of the observable E or in none of them. Thus, the value of the observable A depends upon the set of mutually commuting observables one may consider it with, that is, the

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value of A depends upon the selected set of measurements. In other words, the value of the observable A cannot be thought of as pre-fixed, as being independent of the experimental context actually chosen, as specified, in our example, by the {A, B} or {A, E} frame of mutually compatible observables. Accordingly, the truth value assigned to the associated proposition “a ∈ Δ”—i.e., “the value a of the observable A of system S lies in a certain range of values Δ”—should be contextual as it depends on whether A is thought of in the context of simultaneously ascribing a truth value to propositions about B, or to propositions about E.

18 This state of affairs reflects most clearly the unreliability of the so-called “definite values” principle of classical physics of section 2, according to which, values of physical quantities are regarded as being possessed by an object independently of any measurement context. The classical underpinning of such an assumption is conclusively shown to be incompatible with the structure of the algebra of quantum mechanical observables. Whereas in classical physics, nothing prevented one from considering as if the phenomena reflected intrinsic properties, in quantum physics, even the as if is restricted.Indeed, quantum phenomena are not stable enough across series of measurements of non-commuting observables in order to be treated as direct reflections of invariable properties; the microphysical world seems to be sensitive to our experimental intervention. Now, the selection of a particular observable to be measured necessitates also the selection of an appropriate experimental or measurement context with respect to

which the measuring conditions remain intact. Formally, a measurement context CA(D) can be defined by a pair (D, A), where, as previously, D = |ψ⟩⟨ψ| is an idempotent

projection operator denoting the general initial state of system S and A = ΣiaiPi is a self-

adjoint operator denoting the measured observable. Of course, CA(D) is naturally extended to all commuting, compatible observables which, at least in principle, are co- measurable alongside of A. Then, in accordance with the Bub-Clifton theorem, given the state D of S, D restricted to the set of all propositions concerning A is necessarily 2 expressed as a weighted mixture DA = = 1|ci| |ai⟩⟨ai| of determinate truth-value

assignments, where each |ai⟩ is an eigenvector of A and |ci| = |⟨ψ, ai⟩|, i = 1, …, k. Since DA

is defined with respect to the selected context CA(D), DA may be called a representative 3 contextual state. In other words, DA is a mixed state over a set of basis states that are eigenstates of the measured observable A, and it reproduces the probability distribution that D assigns to the values of A. Thus, with respect to the representative

contextual state DA the following conditions are satisfied:

1. Each |ai⟩ is an eigenvector of A. Thus, each quantum mechanical proposition DAi ≡ P|ai⟩ = |ai⟩⟨

ai|, i = 1, …, k, assigns in relation to CA(D) some well-defined value to A (i.e., the eigenvalue αi

satisfying A|ai⟩ = αi|ai⟩).

2. Any eigenvectors |ai⟩, |aj⟩, i ≠ j, of A are orthogonal. Thus, the various possible propositions

{P|ai⟩}, i = 1, …, k, are mutually exclusive within CA(D). In this sense, the different orthogonal

eigenstates {|ai⟩}, i = 1, …, k, correspond to different values of the measured observable A or

to different settings of the apparatus situated in the context CA(D). 3. Each |ai⟩ is non-orthogonal to D = |ψ⟩⟨ψ|. Thus, each proposition P|ai⟩ whose truth value is not

predicted with certainty is possible with respect to CA(D).

19 It is evident, therefore, that the contextual state DA represents the set of all

probabilities of events corresponding to quantum mechanical propositions P|ai⟩ that are

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associated with the measurement context CA(D). In it the propositions P|ai⟩ correspond in a one-to-one manner with disjoint subsets of the spectrum of the observable A and

hence generate a Boolean lattice of propositions. Thus, the P|ai⟩–propositions are

assigned determinate truth values, in the standard Kolmogorov sense, by the state DA. Accordingly, by freeing symbols P and C from their specific preceding denotations, the following instance of the correspondence scheme is valid: [CC] The proposition that P-in-C is true if and only if there is a state of affairs X such that (1) P expresses X in C and (2) X obtains, where C denotes, in general, the context of discourse, and specifically, in relation to the

aforementioned quantum mechanical considerations, the experimental context CA(D)

linked to the proposition P ∈ LH({DAi}) under investigation.

4.1 Philosophical implications

20 If, however, truth-value assignments to quantum mechanical propositions are context- dependent in some way as the scheme [CC] implies, it would appear that one is committed to antirealism about truth. In our opinion, this assumption is mistaken. The contextual account of truth suggested here is compatible with a realist conception of truth; as I shall argue in the sequel, it subscribes neither to an epistemic nor to a relative notion of truth. Such an account essentially denies that there can be a “God’s- eye view” or an absolute Archimedean standpoint from which to state the totality of facts of nature. For, in relation to the microphysical world, there isn’t a context- independent way of interacting with it. Any microphysical fact or event that “happens” is raised at the empirical level only in conjunction with the specification of an experimental context that conforms to a set of observables co-measurable by that context [Karakostas 2004], [Svozil 2009]. In this respect, empirical access to the non- Boolean quantum world can only be gained by adopting a particular perspective, which

is defined by a determinate sublattice LH({DAi}), or, in a more concrete sense, by the

specification of an experimental context CA(D) that, in effect, selects a particular

observable A as determinate.Within the context CA(D), the A-properties we attribute to the object under investigation have determinate values, but the values of incompatible observables, associated with incompatible (mutually exclusive) experimental arrangements, are indeterminate. Hence, at any temporal moment, there is no universal context that allows either an independent variation of the properties of a quantum object or a unique description of the object in terms of determinate properties. And this yields furthermore an explicit algebraic interpretation of the Bohrian notion of complementarity (a non-Copenhagean, of course), in so far as quantum mechanical properties obtain effectively determinate values—alternately, the associated propositions acquire determinate truth-value assignments—within a

particular quasi-Boolean sub-structure LH({DAi}), whereas the underlying source of quantum mechanical “strangeness” is located in the fact that they cannot be simultaneously realized or embedded within a single Boolean logical structure.

21 Furthermore, the proposed account of truth, as encapsulated by the scheme [CC] of contextual correspondence, ought to be disassociated from an epistemic notion of truth. The reference to an experimental context in quantum mechanical considerations should not be viewed primarily as offering the evidential or verificationist basis for the truth of a proposition; it does not aim to equate truth to verification. Nor should it be

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associated with practices of instrumentalism, operationalism, and the like; it does not aim to reduce theoretical terms to products of operational procedures. It rather provides the appropriate conditions under which it is possible for a proposition to receive consistently a truth value. Whereas in classical mechanics the conditions under which elementary propositions are claimed to be true or false are determinate independently of the context in which they are expressed, in contradistinction, the truth-conditions of quantum mechanical propositions are determinate within a context. On account of the Kochen-Specker theorem, there simply does not exist, within a quantum mechanical discourse, a consistent binary assignment of determinately true or determinately false propositions independent of the appeal to a context; propositional content seems to be linked to a context. This connection between referential context and propositional content means that a descriptive elementary proposition in the domain of quantum mechanics is, in a sense, incomplete unless it is accompanied by the specified conditions of an experimental context under which the proposition becomes effectively truth-valued (see, in addition, [Karakostas 2012]). In other words, the specification of the context is part and parcel of the truth- conditions that should obtain for a proposition in order for the latter to be invested with a determinate (albeit unknown) truth value. In the quantum description, therefore, the introduction of the experimental context is to select at any time t a

specific sublattice LH({DAi}) in the total non-Boolean lattice LH of propositions of a

quantum system as co-definite; that is, each proposition in LH({DAi}) is assigned at time t a definite truth value, “true” or “false”, or equivalently, each corresponding property of the system either obtains or does not obtain. In effect, the specification of the context provides the necessary conditions whereby bivalent assignment of truth values to quantum mechanical propositions is in principle applicable. This marks the fundamental difference between conditions for well-defined attribution of truth values to propositions and mere verification conditions. In the quantum description, therefore, the specification of the experimental context forms a pre-condition of quantum physical experience, which is necessary if quantum mechanics is to grasp empirical reality at all. In this respect, the specification of the context constitutes a methodological act preceding any empirical truth in the quantum domain and making it possible.

22 Nor the proposed contextual conception of truth is a relative notion; the propositions to which it applies are relative. They are relative to a specific maximal sublattice

LH({DAi}) of propositions which are determinately true or false of a system at any particular time. For, as already argued, a quantum mechanical proposition is not true or false simpliciter, but acquires a determinate truth value with respect to a well-defined context of discourse as specified by the state of the quantum system concerned and a particular observable to be measured. Thus, the conditions under which a proposition is true are jointly determined by the context in which the proposition is expressed and the actual microphysical state of affairs as projected into the specified context. What makes a proposition true, therefore, is not that is relative to the context (as an alethic relativist must hold, see, for instance, ) but whether or not the conditions in question obtain. The obtainment of the conditions implies that it is possible for us to make, in an overall consistent manner, meaningful statements that the properties attributed to quantum objects are part of physical reality. In our approach, the reason that a proposition is true is because it designates an objectively existing state of affairs, albeit of a contextual nature.

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BIBLIOGRAPHY

AULETTA, Gennaro [2001], Foundations and Interpretation of Quantum Mechanics, Singapore: World Scientific.

BUB, Jeffrey [2009], Clifton theorem, in: Compendium of Quantum Physics, edited by D. Greenberger, K. Hentschel, & F. Weinert, Berlin; Heidelberg: Springer, 84–86, doi: 10.1007/978-3-540-70626-7\_25.

BUB, Jeffrey & CLIFTON, Rob [1996], A uniqueness theorem for ‘no collapse’ interpretations of quantum mechanics, Studies in History and Philosophy of Science – Part B: Studies in History and Philosophy of Modern Physics, 27(2), 181–219, doi:10.1016/1355-2198(95)00019-4.

BURGESS, Alexis & BURGESS, John P. [2011], Truth, Princeton: Princeton University Press.

CABELLO, Adán [2006], How many questions do you need to prove that unasked questions have no answers?, International Journal of Quantum Information, 04(01), 55–61, doi:10.1142/ S021974990600161X.

DALLA CHIARA, Maria Luisa, GIUNTINI, Roberto, & GREECHIE, Richard [2004], Reasoning in Quantum Theory, Dordrecht: Kluwer.

DEVITT, Michael [2001], The metaphysics of truth, in: The Nature of Truth: Classic and Contemporary Perspectives, edited by M. Lynch, Cambridge, MA: MIT Press, 579–611.

DIEKS, Dennis [1989], Quantum mechanics without the projection postulate and its realistic interpretation, Foundations of Physics, 19(11), 1397–1423, doi:10.1007/BF00732760.

DIRAC, Paul A. M. [1958], Quantum Mechanics, Oxford: Clarendon Press, 4th edn.

KARAKOSTAS, Vassilios [2004], Forms of quantum nonseparability and related philosophical consequences, Journal for General Philosophy of Science, 35(2), 283–312, doi:10.1007/ s10838-004-0927-6.

—— [2007], Nonseparability, potentiality, and the context-dependence of quantum objects, Journal for General Philosophy of Science, 38(2), 279–297, doi:10.1007/s10838-007-9050-9.

—— [2012], Realism and objectivism in quantum mechanics, Journal for General Philosophy of Science, 43(1), 45–65, doi:10.1007/s10838-012-9173-5.

KIRCHMAIR, Gerhard et al. [2009], State-independent experimental test of quantum contextuality, Nature, 460, 494–497, doi:10.1038/nature08172.

MACFARLANE, John [2005], Making sense of relative truth, Proceedings of the Aristotelian Society, 105(1), 305–323, doi:10.1111/j.0066-7373.2004.00116.x.

MCDERMID, Douglas [1998], Pragmatism and truth: The comparison objection to correspondence, The Review of Metaphysics, 51(4), 775–811.

SVOZIL, Karl [2009], Contexts in quantum, classical and partition logic, in: Handbook of Quantum Logic and Quantum Structures, edited by K. Engesser, D. Gabbay, & D. Lehmann, Amsterdam: Elsevier, 551–586, doi:10.1016/B978-0-444-52869-8.50015-3.

VON NEUMANN, John [1955], Mathematical Foundations of Quantum Mechanics, Princeton: Princeton University Press.

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NOTES

1. My goal in the present paper is not to rehearse from a purely philosophical viewpoint the usual objections to a correspondence theory of truth as, for instance, the so-called “comparison objection”, e.g., [McDermid 1998], but to investigate the applicability of the core intuitive notion of a correspondence account of truth within the propositional language of fundamental physics. 2. The principle of value-definiteness has variously been called in the literature as, for instance, “the determined value assumption” in [Auletta 2001, 21, 105]. 3. In justifying the aforementioned term, it is worthy to note that the state DA, which results as a listing of well-defined properties or equivalently determinate truth-value assignments selected by a 2-valued homomorphism on LH({DAi}), may naturally be viewed as constituting a state preparation of system S in the context of the preferred observable A to be measured. This is intimately related to the fact that both states D and DA represent the same object system S, albeit in different ways. Whereas D refers to a general initial state of S independently of the specification of any particular observable, and hence, regardless of the determination of any measurement context, the state DA constitutes a conditionalization state preparation of S with respect to the observable to be measured, while dropping all ‘unrelated’ reference to observables that are incompatible with such a preparation procedure. The importance of the state preparation procedure in quantum mechanics, functioning as a contextual disentanglement process, is analyzed in a detailed manner in [Karakostas 2007, sect.4].

ABSTRACTS

The semantics underlying the propositional structure of Hilbert space quantum mechanics involves an inherent ambiguity concerning the impossibility of assigning definite truth values to all propositions pertaining to a quantum system without generating a Kochen-Specker contradiction. Although the preceding Kochen-Specker result forbids a global, absolute assignment of truth values to quantum mechanical propositions, it does not exclude ones that are contextual. In this respect, the Bub-Clifton “uniqueness theorem” is utilized for arguing that truth-value definiteness is consistently restored with respect to a determinate sublattice of propositions defined by the state of the quantum system concerned and a suitable “preferred” observable. It is suggested that the most natural choice of the latter, especially for confronting the problem of truth valuation in quantum mechanics, results in the determinateness of the observable to be measured. An account of truth of contextual correspondence is thereby provided that is appropriate to the quantum domain of discourse. The resulting account of truth is compatible with a realist conception of truth. Such an account essentially denies that there can be a universal context of reference or an Archimedean standpoint from which to evaluate logically the totality of facts of nature.

La sémantique sous-jacente à la structure propositionnelle de la mécanique quantique des espaces de Hilbert implique une ambiguïté intrinsèque concernant l'impossibilité d'assigner des valeurs de vérité définies à toutes les propositions ayant trait à un système quantique sans générer de contradiction de type Kochen-Specker. Bien que ledit résultat de Kochen-Specker interdise une assignation globale et absolue des valeurs de vérité aux propositions de la mécanique quantique, il n'exclut pas les assignations contextuelles. À cet égard, le théorème

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d'unicité de Bub-Clifton est utilisé pour montrer que le caractère défini des valeurs de vérité est restauré de façon cohérente pour un sous-ensemble déterminé de propositions, défini par l'état du système quantique considéré et une observable préférée appropriée. Il est suggéré que le choix le plus naturel pour cette dernière, en particulier vis-à-vis du problème de l'assignation de valeurs de vérité en mécanique quantique, est que ce soit l'observable sur le point d'être mesurée qui ait une valeur déterminée. On fournit ainsi une conception de la vérité de la correspondance contextuelle qui est appropriée au domaine quantique du discours. La conception de la vérité qui en résulte est compatible avec une conception réaliste de la vérité, qui nie qu'il puisse exister un contexte de référence universel ou un point d'appui archimédien à partir duquel la totalité des faits de la nature puisse être évaluée logiquement.

AUTHOR

VASSILIOS KARAKOSTAS University of Athens (Greece)

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Decisions without Sharp Probabilities

Paul Weirich

I benefitted from discussions with Arif Ahmed, Roger Clarke, Adam Elga, Nils-Eric Sahlin, and Teddy Seidenfeld.

1 Unsharp probabilities arise from sparse or unspecific evidence. For example, meteorological evidence, because unspecific, often does not suggest a sharp probability that tomorrow will bring rain. An agent may assign to rain a range of probabilities going from, say, 0.4 to 0.6. A. Elga argues that unsharp probability assignments may lead an agent to forgo a sure gain [Elga 2010]. In this event, a dilemma arises: the agent may have either unsharp probability assignments that accurately represent evidence, or sharp probabilities that prevent forgoing a sure gain. Should an agent’s probability assignments be faithful to the evidence, or should they promote practical success? This paper maintains that an agent’s probability assignments can attain both goals. It defends a principle of choice that uses imprecise probabilities.

1 Arbitrage

2 Elga’s argument against sharp probabilities begins with a case involving a sequence of choices. In the case, H is a hypothesis. Sally’s evidence concerning H is scant, and she therefore assigns to H the probability interval [0.1, 0.8]. Gamble A wins $15 if H does not hold and loses $10 if H holds. Gamble B wins $15 if H holds and loses $10 if H does not hold. Sally knows that she will receive an offer of A and then an offer of B. She may accept or reject A and afterwards accept or reject B. She also knows that her evidence concerning H will not change during the sequence of offers. The two offers give Sally an opportunity for arbitrage, that is, an opportunity to make a sequence of transactions that ensures a gain; accepting both gambles ensures a gain of $5. The following payoff table shows Sally’s net gain from the two gambles if H is true and if it is false.

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H ∼ H

A − 10 15

B 15 − 10

Net 5 5

3 According to a permissive decision principle that Good proposes, if a set of pairs of probability and utility assignments represent an agent’s mental state, then in a decision problem the agent may choose any option that maximizes expected utility according to some pair of probability and utility assignments in the set [Good 1952, 114]. Amounts of money settle Sally’s utility assignment. So according to the principle, Sally may, when offered the gambles A and B, choose any option that maximizes expected utility according to some probability in the interval that she assigns to H. In particular, the principle may calculate a gamble’s expected utility using either of the interval’s two endpoints. Suppose that for A, a calculation uses the interval’s upper endpoint, whereas for B it uses the interval’s lower endpoint. Using P to stand for probability and EU to stand for expected utility, the results are: (1) If P(H) = 0.8, then EU(A) = (0.8 × −10) + (0.2 × 15) = −5, and EU(∼A) = 0. (2) If P(H) = 0.1, then EU(B) = (0.1 × 15) + (0.9 × −10) = −7.5, and EU(∼B) = 0. 4 According to Good’s principle, Sally may first reject A because this option maximizes expected utility according to (1) and then reject B because this option maximizes expected utility according to (2). However, if she rejects both gambles, she wastes her opportunity for arbitrage. Sally cares about money only, and so if rational does not reject both gambles. The permissive principle is wrong to suggest otherwise, Elga argues.

5 A decision principle that is strict in Elga’s terminology goes from unsharp probabilities to decisions using sharp representatives of unsharp probabilities. For example, the principle MIDPOINT uses the midpoint of a probability interval to reach a decision. Elga rejects such principles because they depart from the rationale for unsharp probabilities. They treat a probability interval as a sharp probability, such as the interval’s midpoint. An acceptable principle of rational choice has to be both permissive about choices taken one by one and also strict about sequences of choices.

6 After rejecting strict decision principles, Elga examines three principles going from unsharp probabilities to decisions that prohibit rejecting both A and B but allow rejecting B in isolation. Although the principles achieve the correct mixture of permissions and obligations, they are defective. The principle NARROW adjusts probability intervals in light of past choices to prevent sure losses in sequences of choices. However, no change in evidence grounds the adjustments in probability intervals, so the adjustments are unwarranted. The principle PLAN states that an agent who begins a sequence of choices should plan coherent choices for the sequence and should then stick to the plan. If Sally rejects A, planning to accept B, then she should accept B after rejecting A. However, as Elga observes, rejecting B after rejecting A has the same monetary consequences as rejecting B when it is offered in isolation. He

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contends that because Sally cares about money only, if she may reject B offered in isolation, she may also reject B when it is offered after rejecting A even if she planned to accept B. The principle SEQUENCE says that a sequence of choices may be irrational despite the rationality of each choice in the sequence. It concedes that for Sally either response to each offer is rational but maintains that rejecting both A and B is irrational. Elga claims that SEQUENCE errs because it permits Sally to reject B offered in isolation, but prohibits her rejecting B if it is part of a sequence of choices that includes prior rejection of A; Sally cares about money only, and rejecting B has the same monetary consequences in both situations.

7 Elga’s argument against decision principles using unsharp probabilities relies on the case of Sally, but this case leaves some important features unsettled. First, Sally’s goals are unclear. Elga specifies that for Sally the utility of money is linear and that Sally cares only about money. The first assumption simplifies calculations of expected utility. The second assumption grounds Elga’s objections to PLAN and to SEQUENCE. I interpret the second assumption so that it attributes to Sally, besides any goals that rationality itself may require, the single basic goal of gaining money and derivative goals concerning means of and opportunities for gaining money.

8 Second, the example does not specify whether Sally decides without forming preferences between her options, or forms preferences and then acts on them. Suppose that she forms preferences that yield her choices and that she rejects both A and B. To represent her preferences, take the symbol for a gamble to stand for having the gamble and the tilde before the symbol for a gamble to stand for not having the gamble. Because Sally rejects A, she prefers some ∼ A-result, either (∼ A & B) or (∼ A & ∼ B ), to all A-results, both (A & B) and (A & ∼ B ). Sally prefers arbitrage to the status quo, so she prefers (A & B) to (∼ A & ∼ B ); she does not prefer (∼ A & ∼ B ) to (A & B). So she prefers (∼ A & B) to both (A & B) and (A & ∼ B ). Because she rejects B, she prefers (∼ A & ∼ B ) to (∼ A & B). Therefore, she prefers (∼ A & ∼ B ) to (∼ A & B), prefers (∼ A & B) to (A & B), and prefers (A & B) to (∼ A & ∼ B ). These are cyclical and so incoherent preferences.

9 If Sally rejects both A and B, the blame for her mistake can be laid on her incoherent preferences rather than on her imprecise probabilities. To target her imprecise preferences, Elga’s argument should assume that Sally makes choices without first forming preferences that direct her choices. I grant this assumption about the example.

10 Third, can Sally predict her choices about the sequence of offers? If she can, backwards induction applies to her choices, and rationality leads her to reject A only if she knows that she will accept B. She has no reason to reject A if she will reject B. However, suppose that Sally cannot predict her choices. Then her rejecting A prior to her rejecting B may be excused; it may arise from her ignorance that she will reject B. To prevent excuses for rejecting both gambles, the argument should assume, and I grant, that when deciding about A, Sally correctly predicts her choice about B. She does not know the outcomes of the gambles but knows her future choice about B.

2 Coherent choices

11 Standard decision theory evaluates a sequence of choices by evaluating its components. The sequence is rational if its components are rational. Rationality is compositional in this sense. A case for compositional evaluation appeals to the consistency of a theory of

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rationality’s standards for single choices and its standards for sequences. A consistent theory does not maintain the rationality of the single choices and the irrationality of a sequence they constitute. It does not permit the choices in the sequence but prohibit the sequence.

12 Elga’s remarks about the decision principle SEQUENCE show his acceptance of the standard method of evaluating sequences of choices. Elga disputes the rationality of single choices resting on imprecise probabilities rather than the sufficiency of the rationality of single choices for the rationality of a sequence they constitute. Nonetheless, Elga’s example challenges rationality’s compositionality. In Sally’s case an irrational sequence of choices apparently arises from choices that are each rational.

13 Suppose that Sally rejects A and then rejects B. These choices are incoherent because they forgo a sure gain. How does the rationality of each choice in a set of choices ensure the coherence of the choices in the set, granting that relevant circumstances are constant and that agents are ideal? Decision principles in the literature use various techniques to achieve coherence.

14 The maximin principle selects for an agent an option that maximizes the agent’s security level. It bypasses probabilities both sharp and imprecise. In the following decision tree, double lines mark the options that maximize Sally’s security level in her sequence of decision problems.

15 Suppose that Sally applies the maximin principle and knows that she will. When offered A, given each of her options, she knows what she will do when offered B. She will accept B if she accepts A, and will reject B if she rejects A. When deciding about A, she chooses the option that maximizes her security level. So she accepts A. Afterwards, she accepts B, as she foresaw.

16 Although strict principles of decision, such as the maximin principle, solve Sally’s decision problems using backwards induction, permissive rules do not because they do not settle future choices. A permissive principle leaves open an agent’s exercise of the permissions it grants.

17 Suppose that an agent is indifferent between options A, B, and C. Breaking ties between these options may lead to incoherent choices. An agent may pick A over B, B over C, and C over A to form a cycle of choices. Also, consider (1) a choice between incomparable options A and B, (2) a choice between incomparable options A and an improvement of B called B + , and (3) a choice between B and B + . A permissive principle may allow choosing A over B + , and also choosing B over A, although it requires choosing B + over B. Taken together, the two permitted choices and the required choice are cyclical.

18 Given indifference or an incomplete preference ranking of options, incoherence threatens for reasons independent of imprecise probabilities. Elga’s argument assumes that in Sally’s case imprecise probabilities generate any indifference or suspension of preference that leads to incoherent choices. I grant this assumption so that his

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argument attacks imprecise probabilities rather than only indifference or incomplete preference rankings.

19 A way for a permissive decision principle to ensure coherence in a sequence of decisions is for it to acknowledge that earlier decisions may affect the consequences of later decisions. Because of earlier decisions, the later decisions may generate an incoherent sequence of decisions and its bad effects.

20 Suppose that rationality is permissive concerning doxastic attitudes formed in light of evidence. Rationality may impose coherence on these attitudes by attending to the consequences of forming new attitudes. Suppose that it is rational to believe or to disbelieve that the universe is infinite. However, if an agent adopts one of these attitudes toward the universe’s size, then rationality prohibits also adopting the other. Even if the evidence allows either attitude, rationality does not permit both because together they are incoherent. Holding a belief that p creates a reason not to hold a belief that ∼ p. The coherence requirements for beliefs become requirements for single beliefs in the context of other beliefs.

21 Similarly, rationality requires permissible preferences to form a coherent group. Given two preferences, rationality bars a third that creates a cycle. The coherence requirements for preferences become requirements for single preferences in the context of other preferences, assuming their rationality.

22 The challenge of Elga’s example is to derive coherence requirements for Sally’s sequence of choices from the requirements for each choice in the sequence. The next two sections show that because Sally makes each choice rationally, considering all its consequences, her choices form a coherent sequence. These sections show that Good’s decision principle for single choices in finite decision problems does not yield incoherent choices in Sally’s case. Despite its permissiveness, it rules out rejecting both gambles.

3 Coordination

23 A person facing a sequence of choices has opportunities to coordinate choices to improve the results of the sequence. A theory of rationality, to hold an agent responsible for making good use of opportunities for coordinating choices, evaluates a choice in a sequence with an eye on the choice’s consequences for opportunities later in the sequence. When evaluating a chess player’s move in a game, rationality considers whether it gains a winning position. A rational chess player whose only basic goal is winning cares derivatively about putting herself in position to win. She may use moves early in a game to achieve a position from which she can checkmate her opponent’s king. Such consequences of the early moves may make them rational.

24 Rationality may allow a person to perform one but not both of two acts. Having done the first, the second becomes impermissible. Exercising a permission may affect the consequences of a subsequent act, and the change in consequences may render it impermissible. Imagine that someone may press button A or press button B but may not press both buttons because that triggers an unwanted explosion. After pressing button A, pressing B is irrational because it produces the explosion. Pressing B after pressing A yields a sequence that rationality prohibits. The bad consequences of the sequence accrue to the component that completes the sequence. Because past acts affect the

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consequences of current acts, evaluation of a current decision looks to the past as well as to the future. Although the decision’s evaluation considers only its consequences, its consequences may depend on the past.

25 Suppose that Jane has only one basic goal, namely, the goal to gain money, and has a choice between a pair of dollar bills today and another choice between another pair of bills tomorrow. The bills available have the serial numbers 1, 2, 3, and 4. Jane is indifferent between the bills. However, she gains an extra dollar if the bills she picks today and tomorrow have adjacent serial numbers, and she knows that today she chooses between bill 1 and bill 2, and tomorrow she chooses between bill 3 and bill 4. Assuming that she picks bill 2 today, when she picks a bill tomorrow, she is not indifferent between bill 3 and bill 4. Picking bill 3 brings an extra dollar. Her choice today affects the consequences of her options tomorrow.

26 Next, suppose that a weather forecaster assigns to rain the probability interval [0.4, 0.6]. The forecaster sells for $0.40 a gamble that pays $1 if it rains and otherwise nothing. Then she buys back the gamble for $0.60, thereby losing $0.20. Each transaction seems justified by Good’s decision principle although rationality, assuming that the forecaster is averse to losing money, prohibits the pair of transactions because they result in a sure loss. In fact, Good’s decision principle does not permit the pair of transactions because, when applied to the second transaction, it considers all the relevant consequences of buying back the gamble. The forecaster wants to avoid a sure loss and can do this by not buying back the gamble. So she should not buy it back. The context of the purchase affects its relevant consequences. That buying the gamble concludes a sequence of transactions that guarantees a sure loss is a relevant consequence of the purchase. The consequence, although not monetary, matters to the forecaster if she is rational.

27 In Sally’s case rejecting both A and B does not incur a loss but instead forgoes a gain. Does it make a difference whether Sally ends up wasting an opportunity for arbitrage or, as the weather forecaster, ensuring a loss? The weather forecaster sells a gamble before buying it back. She is not in her original monetary situation after selling the gamble. Sally is in her original monetary situation if she rejects A, and so rejecting B then appears to be equivalent to rejecting B if it is offered in isolation. Rejecting B has the same monetary consequences in the two contexts. In both contexts rejecting B yields the status quo, no gain or loss. However, strictly speaking, Sally is not in her original situation after rejecting A because she has then forgone the opportunity for arbitrage. Moreover, rejecting A and then rejecting B ensures a loss if possession of the opportunity for arbitrage counts as an advantage equivalent to $5. Rejecting A relinquishes the opportunity for arbitrage, and then rejecting B eliminates the prospect of compensation for relinquishing the opportunity. Framing rejection of A and then rejection of B as forgoing a sure gain rather than as incurring a sure loss does not affect evaluation of this sequence of choices.

28 Sally cares about gaining money. Because she is rational, she cares derivatively about opportunities to gain money. A principle of rationality requires an agent with an end to care about means of achieving the end. The expected-utility principle explicates the requirement. An option’s utility equals its expected utility, as computed from the probabilities and utilities of its possible outcomes. The principle evaluates options as means to ends.

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29 Elga’s objections to PLAN and to SEQUENCE assume a principle of separability. Separability is often defined using conditional preferences. To accommodate Sally’s not forming preferences between her options, its definition may use choices. Sally’s choice about B is separable from her choice about A, if no matter how she settles her choice about A, her choice about B is the same. Because the consequences of rejecting B depend on her choice about A, rationality does not require this type of separability for Sally’s choice about A and her choice about B.

30 Sally, being rational and desiring money, has an aversion to wasting opportunities to gain money. Because she has this aversion, rationality does not require that her choices be independent. Her choice about B may depend on her choice about A. Rejecting A loses the opportunity for arbitrage, and then rejecting B eliminates the prospect of compensation for the loss. Rejecting B does not have this unwanted consequence if accepting A precedes it.

31 A rational agent abandons objectives that serve a basic goal after attaining the basic goal. It may seem that an agent’s evaluation of a possible world should not consider attainment of derived goals. Consequently, it may seem that Sally should be indifferent between any two worlds in which she has the same amount of money. However, Sally, being rational, is averse to a series of decisions that without compensation loses an opportunity to gain $5. A world in which she stays at the status quo without squandering an opportunity for arbitrage is better in her lights than a world in which she stays at the status quo by squandering an opportunity for arbitrage.

32 An objection claims that an evaluation of options that uses worlds as possible outcomes should evaluate worlds using only realizations of basic goals and basic aversions, thus ignoring desires and aversions concerning means. When evaluating rejection of B after rejection of A, the objection holds that Sally should not consider an aversion to wasting her opportunity for arbitrage because it is a derived, not a basic, aversion. The reply to this objection invokes a basic aversion of rational agents, namely, an aversion to wasting opportunities to reach basic goals. Because for Sally gaining money is a basic goal, any world in which Sally wastes an opportunity for arbitrage realizes her basic aversion to wasting opportunities to reach basic goals. An evaluation of the world should consider its realization of this basic aversion.

33 Let ∼ B by itself stand for rejecting B if it is offered alone. Sally does not rank together the world that results from realization of ( ∼ A & ∼ B ) and the world that results from realization of ∼ B. She ranks the first world below the second because she squanders an opportunity to advance her basic goals if she rejects both A and B. Rejecting B when offered in isolation does not have the consequence of squandering an opportunity for arbitrage. The difference in the consequences of rejecting B in the two contexts may justify a difference in Sally’s decisions regarding B in the two contexts. Rejecting B has different consequences for coordination in the two contexts. In contexts where an agent, whose only basic goal is to gain money, has opportunities to coordinate acts to gain money, an act’s monetary consequences do not include all its relevant consequences. A relevant non-monetary consequence is achieving a position to gain money. The agent, if rational, pays attention to such consequences. Should Sally decide about B without regard for her decision about A? Should she consider only the monetary consequences of her decision about B? No, that she squanders an opportunity for arbitrage if she rejects B after rejecting A is a relevant consequence for her.

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34 In Elga’s example, Sally’s opportunity for arbitrage is an opportunity to coordinate her decisions about A and about B so that her sequence of decisions is sure to gain money. Because Sally knows that she will receive an offer of A and then an offer of B, she should exercise her opportunity for arbitrage, unless forgoing it yields prospects at least as good as arbitrage.

35 In Sally’s case, rejecting A and then accepting B are parts of a coordinated sequence of choices that stakes her chance for money on H’s being true. Rejecting A puts Sally in a position to complete this sequence by accepting B. If instead she rejects B, she thwarts coordination of her choices. Rejecting B is less appealing after rejecting A than when B is offered in isolation because Sally cares about her position to gain money. Rejecting B after rejecting A closes her opportunities to gain money.

36 Assuming that for Sally rejecting A is permissible and the sequence rejecting A and then rejecting B is irrational, coordinating her choices by rejecting A and accepting B is worth more to her than rejecting B after rejecting A. Consequently, rejecting B after rejecting A does not maximize expected utility according to any pair of a probability assignment and a utility assignment in her set of such pairs.

37 Using the lowest probability in the interval for H drives down a calculation of the expected utility of B. If P(H) = 0.1, then EU(B) = (0.1 × 15) + (0.9 × − 10) = − 7.5. Because of Sally’s aversion to squandering opportunities to gain money, EU( ∼ B ) < − 7.5. Good’s rule therefore prohibits rejecting B.

38 Attention to consequences besides amounts of money rules out Sally’s rejecting both gambles given a strong aversion to wasting her opportunity for arbitrage. However, some versions of the example weaken this aversion. After rejecting A, Sally may forgo the chance for money that gamble B offers because of a weak aversion to wasting her opportunity for arbitrage. She may without irrationality forgo prospects for gains from accepting gamble B to squash the risk of losing $10 if she accepts this gamble.

39 Attention to a choice’s comprehensive consequences is insufficient to ensure coherent choices in all versions of Sally’s case. The inequality EU( ∼ B ) < − 7.5 must hold to prevent Sally’s rejecting B. However, Sally may reasonably be no more averse to squandering her opportunity for arbitrage than she is averse to losing $5, the monetary value of the opportunity. Moreover, changing Sally’s probability interval for H may lower the value of EU( ∼ B) required to prevent B’s rejection. A revision of the case may use for H the probability interval [0, 1] to make B’s expected utility go from − 7.5 to − 10 when calculated using the interval’s lower endpoint. Sally’s aversion to squandering her opportunity for arbitrage may not be strong enough to make her accept gamble B if its expected utility is as low as − 10. Also, the payoff table for gambles A and B may change to reduce the value of arbitrage and to increase the loss from gamble B if H is false. Sally’s aversion to squandering her opportunity for arbitrage may not be strong enough to eliminate incoherent choices after adjusting the payoffs. The consequences of rejecting B after rejecting A prohibit rejecting B if Sally has a strong aversion to wasting her opportunity for arbitrage but does not prohibit rejecting B if her aversion is weak. Rejecting A does not make rejecting B violate Good’s rule in all versions of the case.

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4 Prediction

40 Rationality’s compositionality and its permissiveness leave few methods of showing that Sally will not reject both A and B. Because of rationality’s compositionality, the coherence of her sequence of choices must derive from the rationality of the choices in the sequence. Rationality’s permissiveness, as expressed by Good’s rule, prevents rationality’s single-handedly grounding predictions of steps in her sequence of choices for applications of backwards induction. Nonetheless, an ideal agent, such as Sally, has resources for preventing incoherence. Her self-knowledge may ground predictions of steps in her sequence of choices, and her predictions may prevent incoherence.

41 In Elga’s example, Sally, being ideal, may predict her choices, her exercises of rationality’s permissions. If she predicts acceptance of B, then rejecting A amounts to putting her chance for money on H rather than on arbitrage. If she predicts rejection of B, then rejecting A is the first step toward wasting her opportunity for arbitrage. Her prediction of her response to the offer of B may ground her response to the offer of A.

42 The consequences of rejecting B depend on prior acts. If Sally rejects A, she thereby forgoes an opportunity for arbitrage. Forgoing the opportunity is not irrational if Sally then accepts B to put her chance for money on H’s being true. She may rationally do this instead of exercising her opportunity for arbitrage. However, if she also rejects B, then she not only rejects arbitrage but also rejects it without gaining as compensation a chance for money if H is true. Rejecting A trades a position from which Sally can guarantee gaining $5 for a position from which she can gain more money if H is true. Then rejecting B trades that position for a position in which no gain is possible. Rejecting both gambles is a mistake because it wastes an opportunity for arbitrage.

43 Not all mistakes are irrational. Some mistakes are excused and so not irrational. Suppose that an agent rejects both gambles and thereby wastes the opportunity for arbitrage. This mistake occurs in two steps. Either rejecting A or rejecting B may be a mistaken step that circumstances excuse. However, Sally is an ideal agent without excuses and rationally avoids mistakes.

44 A compelling argument against Sally’s rejecting both gambles uses her special traits. Given that Sally is a rational ideal agent, and so accurately predicts her choice about B, she does not reject both A and B. After rejecting A, rejecting B may be rational, but the idealizations prevent Sally’s rejecting B. Rejecting A requires as justification a prediction of B’s acceptance. Rejecting A is rational only if Sally foresees accepting B. Rejecting both A and B, given Sally’s rationality, implies a failure to predict her rejection of B, and so a respect in which Sally is not ideal. Given that Sally is rational and ideal, she does not reject both A and B.

45 Suppose that Sally rejects A, accurately predicting that she will accept B. If Sally were to reject B, contrary to her prediction, then her rejecting A would have been a mistake. However, in that case she would have had an excuse for rejecting A. She would not have foreseen her rejection of B. Her lack of foresight, assuming that it is excused, would excuse her incoherent sequence of choices by excusing one of its components. Rationality demands coherence of ideal agents, but accepts excuses for a nonideal agent’s mistakes; its standards take account of an agent’s abilities. Sally’s uncompensated loss of her opportunity for arbitrage would be the price she pays, not

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for having imprecise probabilities, but for not knowing how she will exerciserationality’s permissions.

46 Although Sally is rational and ideal, her hypothetical realization of an incoherent sequence of choices changes her traits. If she retains her rationality while rejecting both A and B, she loses her power to predict accurately her choice about B. However given that Sally is rational and ideal, she correctly predicts her choice about B and so does not reject both A and B. Because Sally is an ideal agent, following Good’s rule does not lead her into this mistake.

47 Good’s permissive decision principle survives Elga’s objections. The principle does not bring unsharp probabilities to grief. Its attention to all an act’s consequences prevents mishaps in some cases, and an agent’s predictions of her own acts prevent mishaps in other cases.

5 Objections and replies

48 Standard decision theory does not prescribe a way of moving from unsharp probabilities to decisions in sequences of decisions. Elga’s case against unsharp probabilities claims that, in fact, no principle of rationality governs the move. Elga supports this claim by refuting contenders drawn from the literature. Sections 3 and 4 defend Good’s permissive decision principle. Does the defense withstand objections?

49 First objection. Applications of Good’s principle in sequences of choices requires keeping track of past decisions and their effect on the consequences of current decisions. This record keeping is demanding. An agent with limited cognitive capacities has a reason to assign sharp probabilities because they eliminate the need to keep track of past decisions. This point counts against a defense of Good’s principle for nonideal agents. However, Elga’s objections treat ideal agents who lack excuses for failing to comply with familiar decision principles, and sections 3 and 4 defend Good’s principle for ideal agents.

50 Second objection. Section 3’s points about ends and means make Good’s decision principle look to the past. Rational decisions look to the future. The future is separable from the past. Ranking options according to their futures produces the same ranking as ranking options according to their comprehensive outcomes—the past does not influence a rational choice among options. Sunk costs do not count, this objection claims.

51 Sunk costs do not count in most cases, however sunk costs count in some cases. Rational deliberation looks ahead to an act’s consequences, but an act’s consequences may depend on past acts and their effect on present opportunities. Suppose that John is indifferent between tea without milk and coffee with milk, but prefers his tea without milk, and prefers his coffee with milk. John pours some milk into a cup. Should he add tea or coffee? Before pouring milk, John is indifferent between pouring tea and pouring coffee. Pouring milk produces a preference for pouring coffee afterwards. Although pouring milk is permissible, and pouring tea is permissible, pouring milk affects the consequences of pouring tea and thereby lowers the utility of pouring tea. An act’s consequences depend on its history, and its consequences affectits present utility.

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6 Against sharpness

52 This paper has defended unsharp probabilities against objections but has not argued positively in support of unsharp probabilities. To close, it offers a brief argument that in some cases rationality not only permits but also requires unsharp probabilities.

53 Although Elga, because of his arguments against decision principles using unsharp probabilities, recommends that Sally assign a sharp probability to H, he does not recommend a particular sharp probability. He maintains just that Sally should assign some sharp probability to H so that she does not waste her opportunity for arbitrage. Rationality does not tolerate an imprecision in Sally’s probability assignment, but tolerates an imprecision about the sharp probability she should assign.

54 Sharp probabilities, conforming to the probability laws, prevent preferences leading to Dutch books but may still generate irrational preferences. They may license some preferences that should not be formed. Suppose that P(R) = 0.80 and P(S) = 0.81, but these are arbitrarily precise probabilities, and evidence does not support the judgment that S is more likely than R. Then the evidence does not warrant preferring a gamble on S to a gamble on R although the sharp probabilities require that preference. Probabilities that are sharper than the evidence warrants lead to preferences that the evidence does not support. Probabilities do not function properly as a guide to action unless they reflect the character of the evidence on which they rest.

55 Although requiring a particular sharp probability given a body of evidence prevents preferences that the evidence does not support, in some cases scant and sparse evidence does not support a particular sharp probability assignment, and fidelity to evidence requires imprecision. In these cases careful application of decision principles prevents their authorizing incoherent sets of choices. Fidelity to evidence and action guidance are compatible goals for probability assignments.

BIBLIOGRAPHY

ELGA, A. [2010], Subjective probabilities should be sharp, Philosophers’ Imprint, 10(5), 1–11, URL www.philosophersimprint.org/010005/.

GOOD, I. J. [1952], Rational decisions, Journal of the Royal Statistical Society, Series B, 14(1), 107–114.

ABSTRACTS

Adam Elga [Elga 2010] argues that no principle of rationality leads from unsharp probabilities to decisions. He concludes that a perfectly rational agent does not have unsharp probabilities. This paper defends unsharp probabilities. It shows how unsharp probabilities may ground rational decisions.

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Adam Elga [Elga 2010] fait valoir qu'aucun principe de rationalité ne mène de probabilités imprécises à des prises de décisions. Il conclut qu'un agent parfaitement rationnel n'a pas de probabilités imprécises. Cet article défend les probabilités imprécises. Il montre comment les probabilités imprécises peuvent justifier des décisions rationnelles.

AUTHOR

PAUL WEIRICH University of Missouri (USA)

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Varia

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Constantes logiques et décision

Saloua Chatti

1 Introduction

1 Le sens des constantes logiques est-il fixé conventionnellement par simple décision ? Ou doit-il s’imposer de lui-même et ne pas dépendre de nos choix individuels ? (1) a été défendue par Wittgenstein et Carnap, (2) a été défendue par Peacocke entre autres. La thèse conventionnaliste a été critiquée notamment par Prior qui a montré qu’elle conduisait à l’admission de connecteurs incohérents ; quant à la thèse anti- conventionnaliste, elle ne rend pas compte des différences notables entre les définitions des constantes dans les systèmes logiques. Compte tenu des impasses auxquelles conduisent ces deux thèses, une position intermédiaire semble être que chaque constante logique doit posséder un sens minimal commun à toutes ses variantes et qui justifie au moins leur appellation commune. C’est cette thèse que je souhaite défendre dans cet essai. Je commencerai par analyser le conventionnalisme et ses limites, ensuite l’anti-conventionnalisme et ses insuffisances, pour finir par dégager les significations minimales des constantes en me basant sur des systèmes déjà existants et en partant des définitions et des règles admises dans ces systèmes.

2 Le conventionnalisme logique

2 Selon Wittgenstein, les constantes logiques n’ont pas des sens bien déterminés car ce sont les règles qui fixent leurs sens. Cette opinion est défendue principalement dans les textes postérieurs au Tractatus où il dit par exemple « la règle ne décrit pas la négation de plus près, mais la constitue » [Wittgenstein 1980, §14, 61]. Dans la mesure où ils sont « constitués » et pas « décrits », les sens des constantes découlent des conventions et des règles grammaticales et peuvent donc être différents d’un système à l’autre. Face à cette diversité, Layla Raïd n’hésite pas à évoquer la notion de décision en disant : Devant ce type de question, Wittgenstein en appelle aux vertus de la décision. Il y a décision car il n’y a aucune nécessité ici. [Raïd 2001, 35]

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3 D’après cette auteure, il n’y a pas de nécessité absolue en raison précisément du caractère conventionnel des significations. Le conventionnalisme exprimé ici est radical en ce qu’il conduit à considérer les propositions logiques comme de simples « prescriptions ». Il est fondé sur la position wittgensteinienne selon laquelle « les règles d’inférence donnent aux signes directement leurs sens, sans que ceux-ci en possèdent un indépendamment des règles » [Engel 1989, 333]. Les règles sont donc constitutives du sens, d’après cette conception. Le libre choix des règles rend les vérités logiques conventionnelles mais ne leur enlève pas leur caractère nécessaire, lequel dépend beaucoup plus de la pratique que d’une réelle essence des vérités logiques et des constantes qui les sous-tendent. Ce conventionnalisme est lié ainsi à la notion de « forme de vie » défendue par Wittgenstein, qui est à l’origine de la décision de considérer ces vérités précises comme « inattaquables » car les attaquer reviendrait à bouleverser de fond en comble notre « forme de vie ». La décision est donc ici motivée par des considérations pratiques, voire « pragmatiques ».Mais ce conventionnalisme peut être contesté car la justification pratique de la nécessité des vérités logiques n’est pas forcément légitime, et donne à la logique un caractère arbitraire qui tue dans l’œuf toute prétention à la vérité et à la rationalité.

4 Quant à Carnap, il considère que les vérités logiques sont analytiques et n’ont aucun contenu empirique. Il parle de convention et de choix en formulant son principe de tolérance, qui s’énonce ainsi : En logique il n’y a pas de morale. Chacun est libre de choisir de construire sa propre logique, i.e., sa propre forme de langage. [Carnap 1937], cité par [Peacocke 1993, 187].

5 Le logicien choisit entre diverses options et décide donc ce faisant de la logique qu’il adopte.

6 Mais on peut montrer, comme Prior l’a fait, que des règles totalement conventionnelles peuvent conduire à des constantes logiques complètement irrecevables comme tonk. Cette constante permet de déduire p tonk q à partir de p, et q à partir de p tonk q. De sorte que son application successive permet de déduire n’importe quoi à partir de n’importe quoi, ce qui est totalement inadmissible. Prior en déduit que les constantes logiques ne peuvent pas être totalement conventionnelles car les conventions peuvent engendrer ce genre d’absurdités : elles ne sont donc ni suffisantes ni pertinentes pour définir les constantes logiques. C’est pourquoi certains logiciens ont caractérisé les constantes logiques en se basant sur la notion de « conception implicite ».

3 L’anti-conventionnalisme logique

7 Selon les tenants de l’anti-conventionnalisme, les vérités logiques ne doivent pas grand-chose à la convention, contrairement à ce que pense Carnap. En effet, pour Peacocke, l’un des représentants de ce courant, la nécessité des vérités logiques n’est pas due à des conventions linguistiques car les conventions ne peuvent pas engendrer les vérités logiques. De même, les constantes logiques ont des sens déterminés qui se reflètent dans les règles qui les caractérisent, lesquelles résultent elles-mêmes de notre compréhension préalable des mots logiques et de ce que Peacocke appelle la « théorie de la détermination » qui permet de donner des valeurs de vérité précises à des énoncés contenant des mots logiques. Ces règles sont les règles d’introduction et d’élimination des constantes. La négation, par exemple, est définie par sa règle

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d’introduction, la réduction par l’absurde, selon laquelle du fait qu’une contradiction (notée ⊥) s’ensuit de p, on est en droit de déduire ∼ p, et par sa règle d’élimination qui affirme que de p et de ∼ p découle une absurdité (⊥) ; la conjonction est définie par sa règle d’introduction qui affirme que de p et de q, on peut déduire p ∧ q ainsi que par ses règles d’élimination selon lesquelles de p ∧ q, on peut déduire p et de p ∧ q on peut déduire q ; les règles d’introduction de la disjonction affirment que de p on peut déduire p ∨ q d’une part et de q on peut déduire p ∨ q d’autre part, celle d’élimination de la disjonction affirme que de p ∨ q et du fait que r s’ensuit de p et que r s’ensuit de q, on est en droit de déduire r. L’implication est définie par sa règle d’introduction qui affirme que du fait que q s’ensuit de p, on est en droit de déduire p ⊃ q, et par sa règle d’élimination, le modus ponens, qui affirme que de p et de p ⊃ q, on peut déduire q.

8 Ces règles sont dites « primitivement irrésistibles » i.e., évidentes par elles-mêmes en raison des conceptions implicites qui leur sont sous-jacentes. Ainsi, ∨ -introduction est justifiée par la conception implicite suivante : Tout énoncé de la forme A ou B est vrai si et seulement si A est vrai ou B est vrai. [Peacocke 1998, 46]

9 Selon Peacocke, c’est notre compréhension du mot « ou » qui conduit à sa table de vérité et aux règles syntaxiques qui le caractérisent et pas l’inverse. La même chose vaut pour tous les autres connecteurs. Ces conceptions interviennent dans les exercices de simulation qui permettent d’évaluer les lois contenant les constantes. Ce sont elles qui aident à fixer les règles : ainsi, la conception implicite correspondant à la négation justifie le fait que ∼ ∼ A implique A, car Tout ce qui est incompatible avec ∼ A, i.e., une chose qui entraîne ∼ ∼ A, doit entraîner A aussi – sous peine que ∼ A ne soit pas la condition la plus faible incompatible avec A. [Peacocke 1987, 164]

10 L’idée primitive sous-jacente à la négation est exprimée ainsi : « dans chaque cas où A n’est pas vraie, ∼ A est vraie » [Peacocke 1987, 164]. Peacocke s’appuie sur une conception réaliste de la vérité ; pour cette raison, il considère, contre les intuitionnistes, qu’une proposition peut être vraie même si elle n’est pas démontrée. Ce réalisme conduit tout naturellement à la bivalence et à une définition de la validité comme « préservation authentique de la vérité » [Peacocke 1987, 157]. De ce fait, c’est parce que les règles d’introduction et d’élimination des connecteurs préservent la vérité qu’elles s’imposent. Cette notion de préservation de la vérité garantit que la définition n’est pas arbitraire, mais bien fondée sur des considérations objectives. Quiconque adopte ce réalisme et la bivalence qui en résulte en viendra à définir les constantes logiques en se basant sur les tables de vérité classiques.

11 On peut donc considérer que pour Peacocke la seule logique correcte est la logique classique. Cette opinion ne laisse pas de place à la décision puisque les conceptions implicites ne sont pas choisies ni déterminées librement, elles sont plutôt ancrées dans notre compréhension des mots logiques.

12 Néanmoins, cette analyse ne tient pas assez compte des différences notables entre les logiques, car les connecteurs logiques ont des sens différents selon les systèmes. Le problème est donc le suivant : peut-on déduire de ces différences que les constantes ne sont plus les mêmes d’une logique à l’autre ? Et qu’est-ce qui justifierait dans ce cas une même appellation ? Pour répondre à ces questions, il faut déterminer les points communs entre les diverses versions des constantes afin de voir où interviennent les décisions dans ce domaine et quelles sont leurs motivations. Je défendrai donc une

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forme de pluralisme modéré et local selon lequel les variantes des constantes logiques partagent un minimum de règles communes qui les rapprochent.

4 Décision et sens des constantes logiques

13 Avant d’analyser ces points communs, considérons certaines formes de pluralisme local existantes dans la littérature. Parmi les tentatives de rapprochement des différents systèmes logiques, on trouve, par exemple, celle de Došen, qui construit un système où il introduit des « règles à deux lignes », pour rendre compte de plusieurs versions d’un même connecteur, selon les éléments qu’elles contiennent . L’implication est ainsi définie par une unique « règle à deux lignes ( → ) » qui caractérise « les implications classique, intuitionniste et pertinente ». La règle en question est la suivante :

14 Dans cette règle, si on « élimine l’affaiblissement [thinning] à droite », on obtient l’implication intuitionniste :

15 Quand en plus, on « élimine l’affaiblissement [thinning] à gauche » :

on obtient l’implication « pertinente du système R d’Anderson & Belnap » [Došen 1989, 367].

16 Néanmoins, les règles doubles de Došen ne rendent compte que des trois systèmes classique, intuitionniste et de la pertinence, ce qui n’est pas suffisant pour rendre compte de l’unité de la logique à travers sa diversité apparente, puisque plusieurs systèmes logiques existants, comme les systèmes modaux et les logiques multivalentes sont laissés à l’écart, malgré leur importance historique et théorique1.

17 Une autre approche est illustrée par la logique dialogique défendue, entre autres, par Shahid Rahman et ses collaborateurs. La stratégie de ces logiciens est de se baser sur deux types de règles : les règles locales et les règles globales, qu’ils se donnent la liberté de modifier afin de rendre compte des diverses variantes des connecteurs. Cette stratégie est intéressante car elle met en jeu directement la notion de décision. Les règles locales définissent les connecteurs au sens strict en « spécifiant ce qui doit compter comme une attaque permise et une possible défense d’un énoncé contenant ces connecteurs » [Rahman & Carnielli 2000, 203] ; les règles « structurelles » ou

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globales caractérisent « les propriétés de la relation de conséquence logique, en décrivant le déroulement général du jeu » [Rahman & Keiff 2008, 4]. En modifiant ces règles d’une manière ou d’une autre, ces logiciens peuvent « donner une expression dialogique à un grand nombre de logiques non classiques et [...] les combiner » [Rahman & Keiff 2008, 2]. Ils les ré-expriment dans un même cadre. Parmi ces systèmes, les auteurs citent « les logiques modales, [...] les logiques libres, [...] les logiques paraconsistantes, [...] la logique linéaire » [Rahman & Keiff 2008, 2]. L’avantage immédiat de cette logique dialogique est qu’elle est à même de rendre compte d’un plus grand nombre de systèmes que les tentatives précédentes. Le système dialogique doit sa flexibilité à son côté « pragmatique » [Rahman & Keiff 2008, 6] revendiqué par ses défenseurs, qui permet de changer les règles en fonction du but fixé. Néanmoins, la flexibilité de cette logique et sa capacité à modifier indéfiniment ses règles lui confèrent un côté conventionnel, voire presque artificiel.

18 Malgré leur intérêt évident, ces tentatives ont leurs limites, car leurs règles sont soit applicables à un nombre restreint de systèmes, soit plus largement applicables mais avec un côté ad hoc. Néanmoins, mon but n’est pas de les critiquer mais, plus modestement, de tenter un autre type de rapprochement, plus naturel, qui au lieu de plaquer sur certains systèmes des règles qui leur sont étrangères, part de ces systèmes pour dégager les points communs entre leurs définitions des constantes afin de montrer ce qui est commun à ces versions, et où et dans quelle mesure les décisions interviennent. Cette méthode a l’avantage du naturel et d’être potentiellement applicable à tous les systèmes ; de fait, je l’applique à la logique mathématique classique, la logique traditionnelle, la logique intuitionniste, les logiques trivalentes et plurivalentes, les logiques modales, les logiques paraconsistantes et les logiques de la pertinence.

4.1 La négation

19 La négation exprime le refus ou l’absence. Dire « Il ne pleut pas », c’est constater l’absence de pluie et refuser d’assentir à « Il pleut ». La négation classique, qui domine depuis Frege et Russell, inverse la valeur de vérité de ce sur quoi elle porte, car p et ∼ p ne sont ni vraies ni fausses ensemble. Néanmoins, bien qu’elle exprime toujours les idées de refus et de privation, la négation peut être moins forte dans les systèmes non classiques. En intuitionnisme, le refus ou la privation portent sur les preuves des propositions. Une proposition n’est considérée vraie que si elle est prouvée. L’absence de preuve ne conduit pas au rejet de la proposition, car la proposition n’est alors pas fausse mais non démontrée. Le rejet total se fait quand p est démontrée fausse, ce qui n’est pas l’équivalent de « p n’est pas démontrée ». D’où le refus du tiers exclu puisqu’il y a désormais trois possibilités : la vérité, la fausseté et l’absence de vérité et de fausseté. La proposition négative devient donc la contraire de la proposition affirmative plutôt que sa contradictoire. Il en résulte que seule p ⊃ ∼ ∼ p est admise mais pas ∼ ∼ p ⊃ p. Par suite, la négation intuitionniste diffère de la négation classique qui admet les deux volets de cette loi. D’autres lois classiques qui font intervenir la négation ne valent plus en logique intuitionniste, comme par exemple l’une des lois de De Morgan, i.e., ∼ ( p ∧ q) ≡ ( ∼ p ∨ ∼ q ), qui est affaiblie en logique intuitionniste car seule l’implication suivante : ( ∼ p ∨ ∼ q ) ⊃ ∼ ( p ∧ q) est valide. De même, les équivalences classiques suivantes : (p ⊃ q) ≡ ( ∼ p ∨ q) ≡ ∼ ( p ∧ ∼ q ) ne sont plus valides en logique intuitionniste qui n’admet que l’un de leurs volets, i.e., les implications : ( ∼ p ∨ q) ⊃ (p ⊃ q) ⊃ ∼ ( p ∧ ∼ q ) . La

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négation intuitionniste apparaît ainsi comme plus faible que la négation classique. Néanmoins, elle partage avec elle certaines lois fondamentales comme la loi de non contradiction ∼ ( p ∧ ∼ p ), qui est valide en intuitionnisme. Dans cette mesure, cette négation n’est pas radicalement différente de la négation classique. Selon Gödel, comme le note [Béziau 2003], elle est comparable à □ ∼ p .

20 On peut également rejeter la bivalence, comme l’a fait Łukasiewicz, ce qui conduit à la modification de la négation dont la matrice fait désormais intervenir trois valeurs : le vrai, le faux et l’indéterminé, noté 1/2. Quand p et ∼ p sont indéterminées, elles ont la même valeur à savoir : 1/2, ce qui va à l’encontre de l’idée d’inversion des valeurs caractéristique de la négation.

21 Néanmoins dans le système de Łukasiewicz, la négation garde quand même certaines de ses propriétés fondamentales comme la loi de la double négation avec ses deux volets : p ≡ ∼ ∼ p . De plus, elle valide les deux lois de De Morgan puisque le biconditionnel est vrai quand ses deux membres ont la valeur 1/2. La décision de Łukasiewicz n’est pas arbitraire puisqu’elle est due principalement à la volonté de préserver la loi de la double négation, qui aurait été invalide si la valeur de ∼ p avait été 0, quand celle de p est 1/2. La négation des systèmes trivalents n’est donc pas radicalement différente de la négation classique puisqu’elle partage avec elle certaines lois fondamentales, mais elle est atténuée. Sémantiquement, l’inversion des valeurs de vérité caractéristique de la négation est présente aussi dans les tables trivalentes mais elle n’est effective que quand les valeurs sont déterminées.

22 De plus, on peut, comme Jean-Yves Béziau l’a fait dans son article [Béziau 2011], interpréter la logique de Łukasiewicz différemment en la transformant en une logique à quatre valeurs de vérité. Partant du constat que Łukasiewicz donne à sa troisième valeur le sens de « possible », J.-Y. Béziau considère que sa logique est une forme de logique modale. Néanmoins, les matrices trivalentes, selon lui, ne sont « pas suffisantes » pour les logiques modales, même « basiques » [Béziau 2011, 2], car elles trivialisent les notions modales. Selon J.-Y. Béziau, le premier choix de Łukasiewicz conduit à donner aux propositions les valeurs suivantes : □α : 0, 0, 0, quand α : 0 − , 0 + , 1, et ◊α : 0, 1, 1 respectivement [Béziau 2011, 3], où « 0 − = nécessairement faux, 0 + = possiblement faux » [Béziau 2011, 4]. Ces deux valeurs sont dites « non-désignées » [Béziau 2011, 3].

23 Pour lui, cette interprétation n’est pas satisfaisante, car la nécessité devient « triviale », puisque « toujours fausse » [Béziau 2011, 3]. La trivialité provient de l’asymétrie entre les valeurs « désignées » (la valeur 1) et « non-désignées » (les valeurs 0 − et 0 + ), car Si nous avons seulement une valeur désignée, nous avons une définition triviale de la nécessité, et si nous avons seulement une valeur non-désignée nous avons une définition triviale de la possibilité. [Béziau 2011, 4, ma traduction]

24 Pour éviter cette trivialité, J.-Y. Béziau propose de remédier à cette asymétrie en adoptant deux valeurs non-désignées (0 − et 0 + ) et deux valeurs désignées (1 − et 1 + ) où les deux dernières valeurs seront interprétées comme suit : « 1 − = possiblement vraie, 1 + = nécessairement vraie » [Béziau 2011, 4]. On peut ainsi éviter la trivialité de la nécessité et de la possibilité et valider certains axiomes cruciaux de la logique modale. Avec ces quatre valeurs, la négation est définie ainsi :

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25 Cette définition rétablit l’idée d’inversion des valeurs de vérité caractéristique de la négation classique. Elle valide aussi la loi de la double négation puisque α est équivalente avec ces quatre valeurs à ∼ ∼ α. Interprétée de cette manière, la négation de cette nouvelle logique à quatre valeurs adaptée de Łukasiewicz (appelée M4N par J.- Y. Béziau) devient encore plus proche de la négation classique dans la mesure où l’inversion des valeurs de vérité se fait dans tous les cas. Néanmoins ces valeurs elles- mêmes sont le résultat de décisions effectuées par J.-Y. Béziau pour éliminer la trivialité des notions modales et valider les axiomes les plus basiques de cette logique. Ces décisions valident aussi les deux lois de De Morgan et les principes de non contradiction et du tiers exclu [Béziau 2011, 9–10], ce qui accentue encore le rapprochement avec la logique classique au niveau de la conjonction et de la disjonction.

26 On trouve aussi chez Quine une logique trivalente appelée « logique de verdict ». Cette logique « de verdict » est dite « primitive » [Quine 1974, 77], car elle transparaît dans les réactions des locuteurs. Quine admet une troisième valeur qu’il nomme « abstention », mais dans les cas où il y a abstention sous p et q, les valeurs de la conjonction et de la disjonction ne sont pas fixées, elles sont notées « ? » ; par contre, s’il y a abstention sous p, il y a abstention aussi sous ∼ p. Quine souligne que « la négation est à la fois une fonction de verdict et une fonction de vérité » [Quine 1974, 77] ; il s’agit donc du même opérateur malgré la différence entre la table de verdict et la table de vérité classique. Cette position diffère de celle de Philosophie de la logique, selon laquelle le fait de changer les règles revient à « changer le sujet » [Quine 1970, 119]. D’après l’exemple qu’il donne, quand p : « c’est une souris » et q : « c’est un écureuil », et quand « aucune n’est affirmée, ni niée » [Quine 1974, 77] p ∧ q provoque très certainement le dissentiment alors que p ∨ q provoquera soit l’abstention, soit l’assentiment. Par suite, la valeur de p ∧ ∼ p sera certainement le dissentiment et celle de sa négation l’assentiment puisque p et ∼ p sont dans tous les cas incompatibles, même quand les propositions sont indéterminées.

27 Le principe de non contradiction n’est pas non plus rejeté dans la logique para- consistante de Da Costa qui ne refuse que la règle ex falso sequitur quodlibet, selon laquelle on peut tout déduire à partir d’une contradiction ; formellement ceci est exprimé de la manière suivante : α,∼ α ⊬ β. Pour ces logiciens, une proposition ne doit pas s’ensuivre de deux propositions contradictoires pour que la déduction elle-même ait un sens. Ce rejet constitue une décision de principe liée à une certaine conception de la déduction et c’est cette décision qui a conduit à modifier le sens de la négation, pas l’inverse. L’invalidation de cette règle a pour conséquences immédiates l’élimination de certaines propriétés de la négation et la relativisation du principe de non contradiction. En effet, la réponse adéquate à la question « Que peut-on déduire d’une contradiction ? » ne peut pas être « tout », car il n’est pas raisonnable selon Graham Priest, par exemple, d’en déduire n’importe quoi. Pour éliminer ce type d’inférences, certains, notamment les dialéthéistes comme Priest, n’hésitent pas à considérer certaines contradictions comme vraies. L’exemple typique de ces

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contradictions « vraies » est le paradoxe du menteur. Malgré cela, ces logiciens refusent d’endosser l’opinion selon laquelle toutes les contradictions sont vraies. Pour eux, le principe de non contradiction n’est pas faux, il est seulement non applicable universellement.

28 Néanmoins la négation para-consistante demeure une forme de négation parce qu’elle satisfait certaines des lois caractéristiques de cet opérateur, par exemple, l’un des volets de la loi de la double négation, qui est ∼ ∼ α ⊃ α et même la loi du tiers exclu α ∨ ∼ α comme le précise Priest qui affirme : Ajouter ces deux axiomes à ceux de la logique intuitionniste positive donne le

système Cw de Da Costa. [Priest 2007, 29] 29 Béziau assimile cette négation paraconsistante à ∼ □p [Béziau 2003].

30 La négation peut ainsi prendre des formes diverses sans cesser d’être une négation, c’est-à-dire une forme d’opposition. Elle peut donc être perçue comme introduisant une opposition plus ou moins forte selon les logiques. Néanmoins, ces formes peuvent être rapprochées malgré leurs différences.

31 Ainsi, dans tous les systèmes, la négation est un opérateur unaire.

32 Deuxièmement, sémantiquement, toutes les négations ont en commun d’inverser les valeurs de vérité des propositions affirmatives soit dans tous les cas, soit dans certains cas.

33 De plus, les différentes négations valident toutes : 1. La loi de la double négation soit dans l’un de ses volets, soit dans les deux. 2. Au moins l’une des lois de De Morgan, voire les deux, soit sous la forme d’une équivalence, soit sous celle d’une implication. 3. Soit le principe de non contradiction soit la loi du tiers exclu, soit les deux.

34 La négation la plus forte est la négation classique, vient ensuite la négation intuitionniste, en troisième lieu la négation para-consistante et enfin la négation des systèmes trivalents.

35 Les différences entre les négations sont donc les conséquences des choix principiels des logiciens non classiques, et ne découlent pas de décisionsarbitraires. Au contraire, les logiciens non classiques tiennent à préserver autant que possible les propriétés de la négation tout en réalisant les objectifs de leurs systèmes.

4.2 La conjonction

36 La conjonction évoque l’idée d’adjonction et de cumul, ou de « juxtaposition » [Quine 1974, 76]. Une conjonction est vraie si chacun de ses éléments est vrai. La conjonction en logique est commutative, car, contrairement à certains usages ordinaires du mot « et », elle ne fait pas intervenir le temps. L’atemporalité de la logique classique est due aux liens étroits entre cette logique et les mathématiques. La conjonction est aussi associative en logique classique et dans les systèmes trivalents, modaux ou autres. Néanmoins, elle aussi est ambiguë, car elle a au moins deux sens, définis par deux groupes différents de règles dans le calcul des séquents de Gentzen, par exemple [Paoli 2005, 314]. Il y a une conjonction « forte » ou extensionnelle qui n’est vraie que quand tous ses membres sont vrais et une conjonction « faible » ou intensionnelle qui est considérée vraie sur la base du fait que l’un de ses éléments pris au hasard est vrai.

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37 Dans la logique de la pertinence de Stephen Read, on retrouve la même distinction entre les deux types de conjonctions, extensionnelle et intensionnelle, la deuxième étant appelée « fusion » et se caractérisant par le fait qu’elle n’admet pas la règle d’élimination classique de la conjonction, mais une règle d’élimination atténuée. Toutefois, la règle d’introduction de la conjonction demeure la même pour les deux variantes, car S. Read dit explicitement que de A et de B (ensemble) on peut déduire A × B, et exprime cela ainsi : X ; Y : A × B est une conséquence immédiate de X : A et Y : B. [Read 2012b, 56, ma traduction]

38 Cette règle est donc commune aux deux types de conjonctions et les rapproche. Il admet aussi la loi de De Morgan suivante : « ∼ ( A × B) est équivalente à ( ∼ A + ∼ B ) » [Read 2012b, 38] où la disjonction est elle aussi intensionnelle. De même il admet l’équivalence entre ∼ ( A × B) et A → ∼ B [Read 2012b, 38], ce qui rapproche encore plus les deux conjonctions, bien que le sens du conditionnel lié à la conjonction classique ne soit pas le même que celui qui est lié à la conjonction appelée « fusion », car S. Read précise que la relation exprimée par → n’est pas vérifonctionnelle [Read 2012b, 38], contrairement au conditionnel classique, symbolisé par ⊃ , par lequel on peut traduire la conjonction classique.

39 Chez Orlov, l’un des premiers logiciens de la pertinence, la fusion admet la première partie de la loi de commutativité de la conjonction soit l’implication suivante : AoB → BoA, et également la première moitié de la loi d’idempotence, soit A → AoA, ainsi que la loi d’associativité ((AoB)oC) → (Ao(BoC)) et (Ao(BoC)) → ((AoB)oC) comme le note Kosta Došen [Došen 1992, 345–346]. Par contre, elle n’admet pas la deuxième partie de l’idempotence, soit la formule suivante : AoA → A, appelée mingle [Došen 1992, 346]. Comme pour la négation, la conjonction des logiques non classiques n’admet qu’une partie des lois de la conjonction classique. Elle apparaît donc comme une conjonction affaiblie, mais elle reste malgré cela une conjonction parce qu’elle partage avec l’opérateur classique un minimum de propriétés communes. Dans les formes affaiblies, ces propriétés se présentent comme des implications.

40 Toute conjonction satisfait donc les propriétés suivantes : 1. la commutatitivité (si on excepte l’usage ordinaire de « et ») ; 2. l’associativité ; 3. la règle d’introduction de la conjonction ; 4. la loi d’idempotence, soit sous forme d’une équivalence soit sous celle d’une implication ; 5. l’une ou l’autre des lois de De Morgan, ou les deux, soit sous forme d’une équivalence soit sous celle d’une implication.

41 Là encore, nous avons des variantes d’un même connecteur, dont la force dépend du nombre de propriétés satisfaites mais qui ont en commun de rendre vrai le complexe quand, d’une manière ou d’une autre, tous ses éléments sont vrais, ce que la règle d’introduction de la conjonction exprime très clairement.

4.3 La disjonction

42 On peut dire la même chose de la disjonction, qui diffère selon les logiques. Il y a globalement trois sens différents de la disjonction : le sens inclusif, le sens exclusif et un sens intensionnel qui est admis par les logiciens de la pertinence essentiellement. La disjonction non exclusive (symbolisée par ∨ ) dit que “p ou q” est vraie si l’une au moins des deux propositions est vraie ; la disjonction exclusive (⊻) par contre est vraie quand l’une des propositions au moins et au plus est vraie ; elle est fausse si les deux

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propositions sont vraies et bien entendu si elles sont toutes les deux fausses. Quant à la disjonction intensionnelle appelée « fission » ( +), elle est définie en termes

d’implication (pertinente) de la manière suivante : « A + B = df ∼ A → B » [Read 1981, 66]. Autrement dit, elle affirme que la fausseté de l’un des éléments implique que l’autre soit vrai, l’implication étant comprise au sens le plus fort : celui de la logique de la pertinence.

43 Toutefois, ces différentes disjonctions n’admettent pas les mêmes règles. Chez les stoïciens, la disjonction est exclusive et n’est vraie que si une seule proposition est vraie. Les stoïciens admettent en effet le syllogisme disjonctif suivant : “p ou q ; or p donc non q” qui n’est valide que si « ou » a le sens exclusif. Néanmoins leur disjonction exclusive n’est pas vérifonctionnelle, comme le précise Suzanne Bobzien [Bobzien 2006, §5.2], car ils ne considèrent que les cas où les éléments sont incompatibles sémantiquement et ne donnent pas la valeur de vérité de « ou » dans le cas où les deux éléments sont vrais. Par contre, en logique moderne, la disjonction exclusive est aussi vérifonctionnelle que la disjonction inclusive, car ses conditions de vérité sont données très précisément par la table de vérité qui lui correspond. Les stoïciens admettent également le syllogisme disjonctif suivant : “p ou q ; or non p ; donc q”, de même que “p ou q ; or non q ; donc p” qui est valide pour les deux types de disjonctions et également pour la disjonction intensionnelle admise par les logiciens de la pertinence puisque le syllogisme disjonctif suivant : “p + q et ∼ p donc q” est précisément sa règle d’élimination [Paoli 2005, 315].

44 Par ailleurs la disjonction inclusive admet « l’addition », i.e., p ⊃ (p ∨ q), contrairement à la disjonction intensionnelle qui n’admet pas la règle “p donc p + q”, et à la disjonction exclusive, qui ne valide pas non plus p ⊃ (p ⊻ q). Cette règle ne vaut donc que pour la disjonction inclusive. Cette dernière admet aussi les deux lois de distributivité qui relient la conjonction et la disjonction, les lois de De Morgan et la loi d’idempotence (p ∨ p) ≡ p, tandis que la disjonction exclusive n’admet que la première moitié de la loi d’idempotence, i.e., la formule suivante : (p ⊻ p) ⊃ p et les premières moitiés des deux lois de De Morgan, i.e., les deux implications suivantes : (∼p ⊻ ∼ q)⊃∼ (p ∧ q) et (∼p ∧ ∼q)⊃∼ (p ⊻ q). Quant à la fission, elle valide (A + A) → A chez Orlov, par exemple, mais elle ne valide « pas toujours A → (A + A) » comme le précise Došen [Došen 1992, 347]. Elle est également associative mais n’admet que la moitié suivante de la loi de commutativité : (A + B) → (B + A) [Došen 1992, 347]. En cela, elle diffère légèrement des deux autres disjonctions qui sont toutes les deux associatives et commutatives au sens plein du terme. Chez Orlov, elle ne valide pas non plus A → (A + B) et B → (A + B) [Došen 1992, 347], ce qui est corroboré par les autres logiciens de la pertinence, comme S. Read, par exemple, qui n’admettent pas l’addition pour la fission. La fission admet une des lois de De Morgan sous la forme suivante : « ∼ ( A × B) est équivalente à ∼ A + ∼ B » [Read 2012b, 38] où la fission est liée à la fusion ; l’autre loi

est sous-jacente à la définition suivante : « A + B = df ∼ ( ∼ A × ∼ B ) » [Read 2012b, 53].

45 Toutefois, malgré ces différences, on peut dégager un certain nombre de points communs entre ces disjonctions puisque : 1. Le syllogisme disjonctif “p ou q or ∼ p ; donc q” est valide pour la fission et pour les deux autres disjonctions dans au moins une interprétation, i.e., si la vérité de la disjonction n’est pas fondée uniquement sur la vérité de l’un de ses membres mais sur la possibilité que l’un ou l’autre soit vrai.

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2. Elles sont toutes les trois commutatives et associatives même si la fission n’admet qu’une partie de la loi de commutativité. 3. Les disjonctions inclusive et exclusive admettent la loi du tiers exclu, mais la fission ne la valide pas toujours [Read 2012b, 81]. 4. Elles admettent toutes la loi de la distributivité de la conjonction par la disjonction (bien que la disjonction exclusive n’admette pas la distributivité de la disjonction par la conjonction). 5. Elles admettent toutes les premières moitiés des deux lois de De Morgan et de la loi d’idempotence. 6. Les disjonctions exclusive et inclusive sont liées au conditionnel, comme la fission l’est à l’implication pertinente, puisque les formules suivantes : (p ⊃ q) ≡ ( ∼ p ∨ q) et (∼p ⊻ q)⊃(p ⊃ q) sont valides en logique classique.

46 Il y a dans toutes ces définitions des points communs, qui sont : 1. La vérité d’un seul élément est suffisante pour rendre la disjonction vraie. Cette caractéristique distingue la disjonction dans tous ses sens, de la conjonction. 2. La vérité de la disjonction ne dépend pas de l’ordre des éléments puisque la disjonction est vraie quel que soit celui de ses éléments qui est vrai, car même la fission peut être vraie quand l’un quelconque de ses éléments est vrai [Read 2012b, 33]. En ce sens, la disjonction dans tous ses sens diffère de l’implication, où l’ordre des éléments joue un rôle crucial. 3. Toutes les disjonctions sont fausses quand leurs deux éléments sont faux, ce qui les distingue de l’équivalence, du conditionnel et de l’implication pertinente.

47 Il y a donc des propriétés communes aux disjonctions puisque certaines lois et règles sont validées dans leur intégralité par ces disjonctions, et celles qui ne sont pas validées intégralement le sont partiellement. Ce qui montre que la différence entre les disjonctions n’est pas radicale.

48 Le privilège dont jouit la disjonction non exclusive en logique classique et dans d’autres systèmes apparaît comme le résultat d’une décision, peut-être motivée par le fait qu’elle est extensionnelle et simple. La disjonction exclusive et la fission sont toutes les deux, chacune à sa manière, plus complexes que la disjonction inclusive, car la disjonction exclusive, par exemple, est exprimée par la formule : (p ∨ q) ∧ ∼ ( p ∧ q) qui ajoute “non (p et q)” à “p ou q”. Quant à la fission, elle est complexe, car elle est définie en termes d’implication pertinente, qui exige plusieurs conditions pour être validée. Nous voyons donc que les modifications de sens sont en réalité des complexifications qui ajoutent des précisions mais ne changent pas radicalement le noyau central du connecteur considéré. La disjonction inclusive est la forme la plus faible, dans la mesure où sa vérité ne dépend que de celles de ses éléments ; vient ensuite la disjonction exclusive qui est plus forte parce qu’elle exige en plus qu’un seul élément soit vrai ; quant à la fission, elle apparaît comme la forme la plus forte, puisqu’elle exige en plus que le lien entre les éléments soit pertinent, de sorte que les valeurs de vérité des éléments ne sont pas suffisantes pour la valider.

4.4 L’implication

49 L’implication évoque intuitivement la notion d’hypothèse ou de condition ; il y a implication quand l’antécédent conduit au conséquent, c’est-à-dire quand il n’est pas vrai que l’antécédent est vrai en même temps que le conséquent est faux, ce qui correspond à ∼ ( p ∧ ∼ q ). Mais cette définition conduit aux paradoxes de l’implication matérielle comme les propositions suivantes : p ⊃ (q ⊃ p), ∼ p ⊃ (p

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⊃ q) et (p ⊃ q) ∨ (q ⊃ p). Pour résoudre ces paradoxes, certains logiciens modaux comme C.I. Lewis ont estimé que le sens de l’implication, qui est censée exprimer la déductibilité et qui est pour cette raison au cœur même de la logique, doit être renforcé de façon à ce que le lien entre l’antécédent et le conséquent garantisse que le conséquent s’ensuit bien de l’antécédent. Pour garantir cette déductibilité, Lewis introduit sa notion d’implication stricte qui dit ceci : « p implique strictement q = il n’est pas possible que p et non q ». S’il n’est pas possible que p et non q, quand p est vraie, q sera aussi vraie, ce qui permettra de déduire q à partir de p. L’implication stricte est réflexive, transitive et non symétrique et admet la loi de contraposition [Hughes & Cresswell 1972, 250]. Ces propriétés la rapprochent de l’implication classique mais l’introduction de la notion de nécessité résulte bien d’une décision. Néanmoins, les paradoxes de l’implication se retrouvent sous une forme modale dans la logique de Lewis, ce qui a conduit à la création de la logique de la pertinence, dont le but est d’éliminer ces paradoxes, quelle que soit leur forme. Pour ces logiciens, le lien entre l’antécédent et le conséquent doit être intensionnel et pertinent ; il est représenté formellement par des « variables communes » [Mares 2006, Introduction]. C’est en effet le lien intensionnel entre l’antécédent et le conséquent qui est le seul garant de la validité de la déduction, car pour ces logiciens, il n’est pas question d’admettre qu’une contradiction implique n’importe quelle proposition ni qu’une tautologie soit impliquée par n’importe quelle proposition. Ces logiques modifient donc le sens de l’implication en refusant de la réduire à une relation extensionnelle, et certaines d’entre elles en viennent même à rejeter le modus ponens dans son sens usuel, où p ⊃ q est exprimé par un conditionnel matériel [Haack 1978, 201]. Néanmoins, en logique de la pertinence, le modus ponens n’est pas rejeté quand l’implication entre p et q est pertinente, comme le prouve S. Read dans son article de 1981, où il dit : Si A et ⌈A → B⌉ sont vraies, alors B l’est aussi, ce qui correspond à MP → . [Read 1981, 67]

50 Donc le modus ponens est accepté et même fondamental quand la première prémisse de cette règle contient elle-même une implication pertinente. De même, certaines propriétés fondamentales de l’implication, comme la transitivité et la réflexivité, sont valides dans la logique de la pertinence comme dans les autres logiques [Haack 1978, 200]. De la même manière, le principe de contraposition est lui aussi admis en logique de la pertinence, bien qu’il soit affaibli, puisque l’axiome 4 d’Orlov, par exemple, est la formule suivante : (A → B) → (¬B → ¬A) [Došen 1992, 342]. Dans les logiques trivalentes, l’implication est également modifiée mais la modification est plus ou moins forte selon les systèmes. Ainsi, la logique de Łukasiewicz admet la transitivité sous la forme suivante : (p ⊃ q) ⊃ [(q ⊃ r) ⊃ (p ⊃ r)]. Celles de Kleene et de Bochvar par contre ne l’admettent pas. La réflexivité est admise dans le système de Łukasiewicz mais pas dans les deux autres. Il y a donc là une différence importante qui est due à des décisions différentes eu égard à la valeur de vérité de l’implication quand p et q ont la valeur 1/2 ; dans ce cas, l’implication chez Łukasiewicz est vraie mais elle est 1/2 chez Kleene et Bochvar. Par contre, le modus ponens (comme règle) continue à valoir pour tous ces systèmes même si la loi correspondante n’est pas valide.

51 Néanmoins, malgré ces différences, l’implication garde certaines propriétés caractéristiques qui se retrouvent dans tous les systèmes. Ce connecteur a, en effet, pour principale caractéristique d’être asymétrique, c’est-à-dire non commutatif, et cette

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caractéristique se retrouve dans tous les systèmes sans exception. De même, il respecte certaines lois et règles à peu près partout2, par exemple : 1. Le modus ponens comme règle, qui est formulé différemment d’un système à l’autre mais reste valide dans tous, même si la loi correspondante n’est pas valide dans certains systèmes. 2. La loi de contraposition, qui est soit complète soit affaiblie, est valide dans à peu près tous les systèmes. 3. La loi de transitivité est admise presque partout, que l’implication soit pertinente, nécessaire ou extensionnelle, car elle représente une composante fondamentale du noyau central de toute implication. 4. Dans tous les systèmes, l’implication traduit l’idée de déductibilité, puisqu’elle est l’expression formelle du concept « s’ensuivre de ». Ce concept est à la base de l’implication, mais les diverses logiques le traduisent différemment selon l’importance qu’elles donnent à la notion de forme et à celle de contenu.

52 Les diverses caractérisations de l’implication ne sont donc que des formes plus ou moins fortes d’un même connecteur. L’implication pertinente est la forme la plus forte, car elle repose sur un lien étroit entre l’antécédent et le conséquent ; vient ensuite l’implication stricte, qui, bien que plus forte que l’implication matérielle, n’élimine pas les paradoxes de l’implication ; les implications des systèmes trivalents sont les plus faibles, car elles introduisent l’indétermination qui affaiblit toutes les propriétés de l’implication et les élimine parfois. Quant à l’implication matérielle, elle est aussi l’une des formes les plus faibles, car elle est fondée uniquement sur les valeurs de vérité des propositions.

5 Les critères de choix des règles définitionnelles

53 Les règles, néanmoins, ne sont pas choisies au hasard. Elles doivent respecter certaines conditions pour que la constante ait un sens. Parmi ces conditions, on peut évoquer l’harmonie. En effet, plusieurs auteurs mettent l’accent sur le fait que les constantes comme tonk sont irrecevables parce que leurs règles d’élimination ne sont pas en harmonie avec leurs règles d’introduction. L’harmonie elle-même, qui, comme le précise S. Read est une notion introduite par Gentzen et reprise par Dummett, se caractérise par le fait que les règles d’élimination doivent être les conséquences des règles d’introduction, de sorte que ces dernières « justifient » [Read 2012a, 1] les premières. Selon les défenseurs de cette conception, c’est parce que ses règles ne sont pas harmonieuses que tonk est un connecteur inadmissible et incohérent. En effet, deux concepts sont confondus dans la formulation de ces règles, la première règle étant une des règles de la disjonction et la deuxième étant une règle de la conjonction. C’est pourquoi S. Read explique l’échec de tonk à être une constante logique en disant que « l’erreur de Prior a été de donner une règle “p tonk q ⊢ q” qui n’était pas justifiée par la règle d’introduction pour tonk » [Read 2012a, 2, présentation modifiée, ma traduction]. Cependant, le même S. Read critique cette notion dans [Read 2008] en montrant que l’harmonie n’est ni nécessaire, ni suffisante pour garantir l’admissibilité d’un connecteur. Ses arguments sont les suivants : 1/ l’harmonie n’est pas suffisante pour garantir la logicité et la consistance d’un connecteur, car dans certains cas, elle est présente mais le connecteur est quand même inconsistant, donc inadmissible [Read 2008, 11]; 2/ elle n’est pas non plus nécessaire, car certains connecteurs parfaitement

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« respectables » et totalement logiques sont caractérisés par des règles non harmonieuses [Read 2008, 12].

54 Pour illustrer (1), S. Read prend l’exemple du connecteur contradictoire • , dont les règles sont harmonieuses [Read 2008, 10], mais qui est inconsistant malgré cette harmonie. (2) est illustré par les règles de Curry caractérisant la nécessité et la possibilité dans le système S4. Ces règles ne sont pas harmonieuses, car ◊E ne découle pas de ◊I mais la complète [Read 2008, 14]. Par suite, ce n’est pas l’absence d’harmonie qui explique l’échec de tonk à être une constante logique mais l’incohérence de ses règles prises ensemble [Read 2008, 6].

55 D’après S. Read, la possibilité est logique, mais plusieurs auteurs mettent en doute la logicité des notions modales. La logicité de la nécessité S4 est validée par certaines règles mais pas par d’autres, car si nous adoptons les contraintes de Došen sur les règles acceptables [Došen 1994, 280], l’opérateur de nécessité S4 est compté comme une constante logique, tandis que si nous adoptons les contraintes de Hacking, il ne l’est pas [Hacking 1979, 297]. [MacFarlane 2009, section 6, ma traduction]

56 Sa logicité peut aussi dépendre du type de critères propres à délimiter la notion de constante logique. Ainsi, le critère d’invariance sous les permutations dans un domaine d’objets n’intègre la nécessité du système S5 au sein de la logique que quand il est étendu aux « permutations dans un domaine de mondes possibles » [MacFarlane 2009].

57 Ce critère d’invariance par permutation, adopté, entre autres, par Tarski délimite l’ensemble des constantes logiques sur la base de leur « insensibilité aux identités particulières des objets » [MacFarlane 2009, section 5]. Il exprime mathématiquement la généralité et la neutralité de la logique. Dans sa forme initiale, cependant, il ne s’applique pas aux connecteurs propositionnels, car les extensions de ces derniers ne sont pas « des objets au sens usuel » [MacFarlane 2009, section 5], mais des valeurs de vérité. C’est pourquoi Gila Sher préfère une formulation en termes d’une disjonction où le premier élément rend compte des connecteurs extensionnels et le deuxième est sa reformulation propre du critère d’invariance, comme le note Dutilh Novaes [Dutilh Novaes 2014, 91].

58 Le critère de Tarski inclut au sein de la logique plusieurs notions spécifiquement mathématiques et d’autres dont le caractère logique est contestable. C’est pourquoi les logiciens qui le corrigent veulent restreindre sonapplicabilité. Mais C. Dutilh Novaes souligne une inadéquation plus fondamentale car, pour elle, [...] l’invariance par permutation est dès le départ une approche déviée de la nature de la logique. Comme Tarski lui-même l’a noté dans sa conférence de 1966, le critère d’invariance par permutation conduit à une classe de « constantes logiques » putatives qui sont essentiellement sensibles uniquement au nombre d’éléments dans les classes d’individus [...]. [Dutilh Novaes 2014, 82, ma traduction]

59 Selon elle, ce critère « sous-génère », car il exclut des notions appartenant à la logique comme certaines conceptions de la nécessité. Par suite, elle considère qu’il n’est pas nécessaire pour délimiter la logique. Pour justifier cette opinion, elle se base premièrement sur la pratique des logiciens en disant : Si un critère de logicité nous fait considérer les opérateurs modaux correspondants comme non logiques, cela semble être un véritable cas de sous-génération du point de vue des pratiques. [Dutilh Novaes 2014, 95] et plus loin

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Harman (1972) suggère que nous n’avons pas besoin de considérer la logique modale comme « logique » et par conséquent nous ne devrions pas la considérer comme de la logique. Je suggère ici que si nous faisons cela, en tant que philosophes, nous exclurions une partie vibrante des pratiques logiques du domaine de l’analyse, ce qui, je pense, n’est pas recommandé. [Dutilh Novaes 2014, note 14]

60 Grossièrement résumé, l’argument semble dire : puisque les logiciens étudient la nécessité, il semble raisonnable de la considérer comme faisant partie dela logique.

61 Cet argument peut être contesté, car on pourrait aussi bien l’appliquer à toutes sortes de logiques non classiques, comme la logique épistémique ou la logique déontique, dont la neutralité est pour le moins douteuse. Le fait que les logiciens s’y intéressent et les étudient ne garantit pas, à lui seul, que ces systèmes possèdent la neutralité et la généralité de la logique. Il n’est donc pas décisif, même si d’une certaine façon, il est légitime en tant qu’il montre que les logiciens peuvent déterminer, par leur pratique propre, l’étendue et la nature de leur domaine d’étude.

62 Néanmoins, sa critique repose aussi sur d’autres arguments liés aux structures admises dans les systèmes modaux. Pourquoi, interroge-t-elle, la nécessité d’un système modal donné correspondant à une relation d’accessibilité « universelle » (« chaque monde “voit” tous les mondes »), « vide » (« aucun monde ne “voit” aucun autre monde »), ou « d’identité » (« chaque monde ne “voit” que lui-même ») est-elle logique dans ces cas, mais devient-elle non logique quand les structures changent ? [Dutilh Novaes 2014, 92]. Le fait que l’opérateur de nécessité ne soit pas logique quand la structure n’est pas l’une de celles citées plus haut, par exemple dans S4, lui pose un problème car elle se demande « quelles motivations indépendantes pourraient justifier que les opérateurs modaux de S4 ne sont pas considérés comme logiques, alors que leurs doubles [counterparts] interprétés dans des structures universelles le sont » [Dutilh Novaes 2014, 94]. Cette critique se distingue des autres par son refus du fait que la structure du système soit le facteur décisif pour juger de la nature logique ou pas de la nécessité.

63 Quelle que soit sa pertinence, que certains contestent3, elle montre que dans tous les cas, les logiciens partent d’une certaine idée de la logique et prennent leurs décisions sur cette base, dans tous leurs choix. Les décisions interviennent donc à plusieurs niveaux : au niveau des règles utilisées pour caractériser les constantes logiques, mais également des critères utilisés pour caractériser la notion de logicité elle-même, mais dans tous les cas, elles ne sont pas arbitraires et découlent de conceptions préalables eu égard à la nature même des constantes et de la logicité. En effet, les propriétés fondamentales des différents connecteurs ne sont pas choisies au hasard, elles sont le reflet des conceptions préalables que les logiciens se font de ces constantes. Les divergences qu’on peut trouver entre les différentes variantes des connecteurs sont les conséquences des choix effectués par les logiciens quant aux notions fondamentales de déduction, de vérité, d’opposition et de logicité.

6 Conclusion

64 En conclusion, les constantes logiques ne sont pas définissables par simple convention et leurs sens dans les différents systèmes gardent quelque chose de commun qui se manifeste à travers les sens intuitifs des expressions qui les désignent et dont l’origine est linguistique, mais aussi dans les règles communes qui les caractérisent, même si ces règles sont atténuées et affaiblies dans certains systèmes. Malgré la diversité de leurs

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sens, les constantes logiques demeurent reconnaissables comme telles dans la mesure où on peut retrouver un noyau commun dans toutes les variantes d’une même constante. Chaque opérateur oscille ainsi entre plusieurs versions, de la plus forte à la plus faible. Les divergences qu’on observe sont donc des différences de degré et non de nature ; elles sont dues aux contextes traités, aux décisions prises par les logiciens en faveur de tel ou tel système de règles ou de tel ou tel principe fondamental, décisions qui sont elles-mêmes motivées par les conceptions de la vérité ou de la déduction que les auteurs privilégient par rapport à d’autres. Ce sont ces conceptions fondamentales qui conduisent à des décisions de principe adoptées en amont et motivent les choix des règles caractérisant les constantes logiques dans les différents systèmes. La notion de décision a donc un rôle à jouer dans la caractérisation des constantes logiques, mais il n’y a pas de décision arbitraire créant une logique de toutes pièces et les constantes comme tonk se trouvent bannies du simple fait qu’aucune intuition et aucune caractérisation cohérente et acceptable ne leur correspondent.

BIBLIOGRAPHIE

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HUGHES, George E. & CRESSWELL, Maxwell J. [1972], An Introduction to Modal Logic, London : Methuen and Co Ltd.

MACFARLANE, John [2009], Logical constants, Stanford Encyclopedia of Philosophy, edited by Zalta, E. N., URL http://plato.stanford.edu/archives/win2008/entries/logical-constants/.

MARES, Edwin [2006], Relevance logic, Stanford Encyclopedia of Philosophy, edited by Zalta, E. N., URL http://plato.stanford.edu/edu/entries/logic-relevance/.

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PAOLI, Francesco [2005], The ambiguity of quantifiers, Philosophical Studies, 124(3), 313–330, doi : 10.1007/s11098-005-7777-x.

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PRIEST, Graham [2007], Paraconsistency and dialetheism, dans The Many Valued and Nonmonotonic Turn in Logic, édité par D. M. Gabbay & J. Woods, North-Holland, Handbook of the History of Logic, t. 8, 129–204, doi :10.1016/S1874-5857(07)80006-9.

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NOTES

1. Dans la même optique, Sambin et al. ont construit un système différent appelé «logique basique» où ils intègrent les logiques «classique, intuitionniste, quantique et linéaire non- modale» [Sambin, Battilotti et al. 2000, 979]. Néanmoins, ce système pose la question suivante: qu’est-ce qui justifie que le rapprochement se fasse entre ces systèmes particuliers et pas les autres, sachant que la logique quantique non distributive, par exemple, est pour le moins marginale?

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2. Les seules exceptions étant les deux systèmes de Bochvar et de Kleene qui sont très spéciaux, car ils invalident à peu près toutes les lois logiques. 3. L’un des rapporteurs la conteste en évoquant [van Benthem & Bonnay 2008].

RÉSUMÉS

Dans cet article, j'analyse le problème des significations des constantes logiques. Ces significations sont-elles fixées conventionnellement comme le suggèrent Carnap et Wittgenstein, ou bien doivent-elles s'imposer à tous et ne pas dépendre de décisions préalables ? Après avoir examiné le conventionnalisme de Wittgenstein et Carnap et l'anti-conventionnalisme de Peacocke selon lequel les sens des constantes logiques reposent sur des conceptions implicites, je montre que les deux thèses sont également critiquables. La première ne résiste pas à l'incohérence du connecteur « tonk », inventé par Prior, dont les règles montrent que la convention ne peut pas déterminer à elle seule les significations des constantes logiques, la deuxième ne tient pas assez compte des divergences importantes entre les logiques. En me basant sur différents systèmes logiques, je présente de nouveaux arguments pour défendre une position intermédiaire selon laquelle chaque constante logique se déploie en diverses variantes qui forment un spectre allant de la version la plus forte à la version la plus faible. Dans ce cadre, le concept de décision joue un rôle en logique, mais les décisions sont prises en amont, en fonction de certaines conceptions touchant la vérité, la déduction et les critères de logicité adoptés par les logiciens, et tiennent compte des intuitions fondamentales liéesà chaque constante.

In this article, I examine the problem of the meanings of the logical constants. Are these meanings conventional as suggested by Carnap and Wittgenstein, or should we say that they are assigned and do not depend on preliminary decisions? After studying the conventionalism defended by Wittgenstein and Carnap and the anti-conventionnalism endorsed by Peacocke, according to which the meanings of the logical constants depend on some implicit conceptions, I show that both theses can equally be criticized. The first one does not resist the incoherence of the connective “tonk” invented par Prior, whose rules show that the convention cannot by itself fix the meanings of the logical constants, the second does not take sufficient account of the important differences between the logical systems. By relying on different logical systems, I give some new arguments to defend an intermediary position according to which each logical constant has different variants which go from the strongest version to the weakest one. In this context, the concept of decision plays a role in logic but the decisions depend on some previous fundamental conceptions with regard to truth, deduction and the criteria of logicality which are endorsed by the logicians, and they take into account the fundamental intuitions related to each constant.

AUTEUR

SALOUA CHATTI Université de Tunis (Tunisie)

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Insaisissable Belle au bois dormant

Laurent Delabre et Léo Gerville-Réache

1 Introduction

1 Le paradoxe probabiliste de la Belle au bois dormant n’est pas une récréation mathématique. C’est une véritable boîte de Pandore qui nous ramène toujours aux zones d’ombre de chaque théorie invoquée en vue de sa résolution. En ajoutant une drogue à effet amnésique au protocole anodin d’une expérience de pensée, nous ranimons soudain des controverses très profondes liées aux concepts de probabilité, de rationalité, d’identité, de connaissance, de temps ; nous revisitons des principes, moins solides qu’ils en avaient l’air, et participons à une aventure épistémologique captivante.

2 Rappelons le problème. Ce dimanche soir, des chercheurs vont endormir pendant quelques jours la Belle au bois dormant ; puis ils lanceront une pièce de monnaie équilibrée. Selon le résultat, ils interrompront brièvement le sommeil de la Belle soit une, soit deux fois : si face, un réveil le lundi ; si pile, un réveil le lundi, un autre le mardi. Chaque fois, ils auront un entretien avec elle, puis la rendormiront à l’aide d’une drogue qui lui fera complètement oublier ce réveil. Voici que la Belle, qui connaît tout ce protocole, se réveille au cours de l’expérience, incapable de savoir si c’est lundi ou mardi. On lui demande alors : « À quel degré devez-vous croire que la pièce est tombée sur face ? »

3 Complétons l’énoncé : si on est lundi, dès que la Belle a répondu à cette question principale, on lui annonce qu’on est lundi et on lui repose la question.

4 Selon les « tiéristes1 », qui semblent majoritaires, une Belle parfaitement rationnelle doit répondre 1/3 à la question principale, puis 1/2 à la question subsidiaire du lundi. Peu nombreux, les demistes répondent 1/2 à la première question, 2/3 à la seconde. Ce demisme traditionnel est concurrencé aujourd’hui par le « double-demisme », ou demisme de la conservation de la croyance, qui répond 1/2 aux deux questions. Dans tous les camps se trouvent des philosophes attachés au bayésianisme, mais aussi des insatisfaits. Aucun consensus ne s’est dégagé, toutes ces contrariétés révèlent un paradoxe redoutable. Quelques travaux, qui ne seront pas présentés ici, prétendent le

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résoudre par une désambiguïsation de son énoncé ou l’acceptation de plusieurs réponses2.

5 Nous allons éclairer, questionner, prolonger et critiquer trois des nombreux arguments de la littérature : l’arbitrage fréquentiste, l’analogie avec le problème de Monty Hall, et la leçon des « compagnons » de la Belle. Ces pistes de réflexion donneront un petit aperçu du vaste et riche débat en cours et introduiront aussi des idées inédites.

2 L’arbitrage fréquentiste

6 Ce premier argument, déjà évoqué par Adam Elga, le philosophe qui a popularisé la Belle au bois dormant [Elga 2000], est notamment complété et défendu par le mathématicien Jean-Paul Delahaye [Delahaye 2003]. Il s’agit d’un raisonnement tiériste à l’origine, même si plus tard il inspire des avis moins tranchés.

7 Reformulons d’abord l’argument demiste bayésien de David Lewis, au centre de la critique tiériste : la Belle, qui estimait dimanche à 1/2 la probabilité de face (ontologique puis épistémique), n’apprend rien de pertinent pour l’issue pile/face à son réveil. Elle est réveillée, l’expérience est en cours, rien de surprenant. Elle sait que « ce jour est lundi ou ce jour est mardi », mais ce n’est qu’une évidence indexicale impuissante. L’inertie doxastique apparaît donc nécessaire et rationnelle : la Belle doit encore croire au degré 1/2 en l’obtention de face. En revanche, l’information « on est lundi est pertinente, la Belle qui la reçoit doit augmenter la probabilité de face » jusqu’à 2/3, suivant la loi de conditionalisation bien connue [Lewis 2001].

8 Pour Delahaye, ces résultats, obtenus au mépris du décompte le plus élémentaire des réveils en tant qu’événements réalisés lors de très nombreuses répétitions de l’expérience, sont faux et montrent les limites des révisions bayésiennes pourtant salutaires en d’autres circonstances. La Belle qui se sait engagée dans une série d’expériences sait aussi qu’elle existe en double dans les expériences-pile, elle sait par exemple qu’il est dans son intérêt de parier sur pile à chaque réveil. Son espace privé de probabilité se déforme en partie, s’adapte aux probabilités fréquentielles. Les réponses tiéristes s’imposent alors à elle. Lorsqu’on lui annonce qu’on est lundi, un glissement bayésien a bien lieu mais ne fait qu’annuler cette anamorphose dite effet de loupe qui avait rendu pile deux fois plus probable que face.

9 Ce retour au fréquentisme est louable mais pour le moins téméraire, puisqu’il prétend démêler un problème fortement noué de localisation d’un sujet (potentiellement) amnésique dans des mondes possibles et dans le temps en répétant une expérience qui se voulait unique. Mais ce qui nous intéresse est un point précis. Il est un fait que si l’expérience de la Belle est répétée un grand nombre de fois, la fréquence de réveils- face sera deux fois moindre que la fréquence de réveils-pile. Mais dans quelle mesure ces fréquences sont-elles des probabilités et constituent-elles un argument en faveur de la position tiériste ?

10 La répétition du scénario sur une infinité de semaines produit deux séries de résultats :

11 • L’une est une suite d’expériences hebdomadaires et donc de tirages équiprobables et indépendants d’une pièce. La série obtenue est par exemple : P − F − P − P − F − F − F − P − F − P − P − P − F − F... Elle contiendra, sur une infinité de semaines, une fréquence égale de piles et de faces (1/2 − 1/2).

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12 • L’autre est une succession de réveils, conséquence directe, déterminée par le protocole, de la série d’expériences précédente. En partant de notre exemple, on obtient la série de réveils suivante : PP − F − PP − PP − F − F − F − PP − F − PP − PP − PP − F − F... Elle contiendra sur une infinité de semaines une fréquence deux fois moindre de réveils-face que de réveils-pile (1/3 − 2/3).

13 Une lecture attentive des deux séries dévoile deux différences importantes. Si les fréquences calculées sur la première série le sont sur une suite de réalisations indépendantes dont le nombre est égal au nombre de semaines, les fréquences calculées sur la série de réveils le sont sur une suite de réalisations dépendantes dont le nombre total est aléatoire. Si, pour la première série, on est dans le cadre traditionnel de la loi des grands nombres et de la convergence de la fréquence vers la probabilité, la seconde série pose une question : dans quelle mesure la dépendance des réveils et le nombre aléatoire de réveils permettent-ils d’affirmer que la fréquence converge vers une probabilité ?

14 L’interprétation du calcul de la fréquence de réveils-face et/ou de réveils-pile n’est pas claire. Rappelons que la définition de la probabilité comme fréquence limite d’un événement trouve son origine dans la loi des grands nombres, qui concerne une somme de variables aléatoires (de Bernoulli par exemple) indépendantes et identiquement distribuées divisée par le nombre déterministe de ces variables. La probabilité est donc définie comme un quotient vérifiant certaines conditions. Notre problème est de comprendre, dans le cas de la Belle, si la fréquence proposée entre dans le cadre d’une définition (éventuellement élargie) de la probabilité au sens fréquentiste.

15 Initialement, on définit la probabilité comme la limite suivante :

où les Xi sont des variables aléatoires de Bernoulli indépendantes et identiquement

distribuées. Ici, Xi = 1 si la pièce tombe sur face la semaine i, 0 sinon. Pour la Belle, aux réveils, on s’intéresse à :

16 Cette limite vaut assurément 1/3 si p = 1/2. Mais la question est de savoir si :

est une probabilité, et en quel sens. Pour résumer, quand on divise une somme de variables aléatoires de Bernoulli indépendantes et identiquement distribuées par n, cette statistique converge vers une probabilité qui est la probabilité que chaque variable aléatoire prenne la valeur 1. Mais quand on divise cette même somme par le nombre aléatoire de réveils , qu’obtient-on ?

17 In fine, d’un côté, à chaque expérience P(Face) = 1/2 ; de l’autre côté, la fréquence de réveils-face sur une infinité de réveils est P(Face)/(2 − P(Face)) = 1/3. Reste à savoir si P(Face)/(2 − P(Face)) est une probabilité. Si oui, est-ce une probabilité au sens fréquentiste ? Si oui, est-ce la « bonne » réponse à la question posée à la Belle ?

18 La rivalité des interprétations ontologique et épistémique ne doit pas faire oublier les multiples conceptions philosophiques de la probabilité. Même au sein du fréquentisme,

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plusieurs axiomatiques existent. Selon von Mises [Bienvenu 2007, 145–146], une probabilité fréquentielle doit vérifier que : • la fréquence relative d’un ensemble d’éléments caractérisés dans une suite de référence admet une limite (axiome d’existence de limites) ; • cette limite est invariable dans toute suite partielle issue de la suite de référence au moyen d’une méthode de sélection des éléments de la suite partielle par « choix de position » (axiome d’irrégularité).

19 Manifestement, si l’axiome d’existence d’une limite est vérifié sur la série des réveils répétés, l’axiome d’irrégularité ne l’est pas. Aussi, 1/3 n’est pas une probabilité- fréquence au sens de von Mises. Un sens pas toujours retenu. Dans sa proposition de définition, Reichenbach ne fait aucunement appel à l’axiome d’irrégularité [Bienvenu 2007, 145–146]. La probabilité est pour lui fondamentalement associée à des paris : la mise doit nécessairement découler du constat d’une fréquence sur une section finie d’une suite d’événements supposée prolongeable à l’infini. Ainsi, au sens de Reichenbach, 1/3 est bien une probabilité fréquentielle... mais de quel événement ?

20 La réponse se trouve peut-être dans la position de Weatherford à propos du principe d’indifférence : Les difficultés empiriques qui ont discrédité le principe d’indifférence sont entièrement dues au fait que beaucoup ont confondu la probabilité de choisir un succès avec la probabilité d’être un succès. [De Scheemaekere 2011, 64]

21 Weatherford pointe, ici pour la question du principe d’indifférence, les différences de conception entre von Mises et Reichenbach. Pour ce dernier, la probabilité de choisir un succès et la probabilité d’être un succès ne font qu’un. Pour von Mises, une différence existe et c’est peut-être cela que traduit l’axiome d’irrégularité.

22 Ainsi, dans le problème de la Belle, si l’on reprend la série de réveils et si l’on tire un réveil avec équiprobabilité, la probabilité de tirer un réveil-face est bien 1/3. Cela pose pourtant deux derniers problèmes : • Si l’on considère une série infinie de réveils, une telle procédure de sélection équiprobable est impossible. En effet, il n’existe pas de loi de probabilité uniforme sur un ensemble infini d’objets. On peut néanmoins lever cette difficulté en considérant un grand nombre de réveils plutôt qu’une infinité. • Dans quelle mesure, à son réveil, la Belle doit se référer à la probabilité de « choisir un succès » et pas à la probabilité « d’être un succès » ?

23 Cette question nécessiterait encore bien des développements. L’important est de voir que, quand il prétend répondre à la question principale de l’entretien, l’argument fréquentiste tiériste n’a pas de fondement sous l’axiomatique de von Mises, que la fréquence de réveils-face est une probabilité au sens de Reichenbach, mais qu’une Belle inspirée par Reichenbach n’est pas encore tirée d’affaire. Le demisme traditionnel a donc un espoir. Pas pour longtemps.

24 Transformons la série de réveils que nous avons précédemment donnée en éliminant ceux qui ne satisfont pas la condition « a lieu lundi » :

PP − F − PP − PP − F − F − F − PP − F − PP − PP − PP − F − F 25 Naturellement, cette série de réveils-lundi est celle des face/pile du dimanche soir : P − F − P − P − F − F − F − P − F − P − P − P − F − F 26 Cela signifie que la Belle qui sait qu’on est lundi et croit en face au degré 1/2 peut sereinement affirmer que ce degré correspond à une probabilité fréquentielle au sens

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de von Mises et de Reichenbach. Ce n’est pas un hasard si très peu de philosophes après Lewis argumentent en faveur de P(Face|Lundi) = 2/3 et s’ils sont peu suivis par la communauté : certes, les approches objectivistes ne semblent pas pouvoir départager demistes et tiéristes en ce qui concerne la question principale, mais cette réponse 2/3 à la question subsidiaire paraît si étrangère à l’analyse fréquentiste qu’elle devient également suspecte aux yeux des bayésiens.

27 D’autres arguments discréditent la réponse 2/3. Reprenons et prolongeons le plus fameux d’entre eux, exposé pour la première fois par Elga. Lorsque la Belle apprend qu’on est lundi, elle ne fait que récupérer un savoir que l’expérience et son protocole lui ont ôté et doit simplement croire en l’obtention de face à un degré égal à la propension à tomber sur face d’une pièce équilibrée. En effet, la voici réveillée lundi, événement qui devait assurément arriver ; elle sait qu’elle n’est pas encore amnésique, qu’aucun accident cognitif ne la trompe ; la pensée que demain mardi peut avoir lieu un réveil ne peut pas la gêner. Plus rien d’important ne la différencie d’un sujet extérieur au protocole qui doit obéir à un principe d’alignement des probabilités ontologique et épistémique. Remarquons que le déroulement de l’expérience ne dépend pas du résultat du lancer de la pièce tant que mardi matin n’est pas venu. Imaginons alors un scénario similaire où la pièce n’est lancée que dans la nuit de lundi à mardi afin de déterminer si un autre réveil doit avoir lieu avant que l’expérience ne prenne fin : cette légère variation des règles, connue par la Belle, ne peut pas changer ses réponses et en particulier, quand elle est réveillée lundi et qu’elle en est informée, elle doit clairement croire que la pièce qui sera lancée dans quelques heures a une chance sur deux de tomber sur face. On peut même l’inviter à lancer elle-même la pièce, puisque de toute façon la drogue va lui faire oublier la journée du lundi : une fois que la pièce est dans sa main, la Belle peut-elle raisonnablement estimer à 2/3 la probabilité d’obtenir face ? Nous pensons que non.

28 Le prolifique demiste bayésien Darren Bradley [Bradley 2011] a développé une argumentation qui, selon lui, clarifie la critique trop hâtive que Lewis opposait à cet argument solide tel qu’il était présenté par Elga. Quand on annonce à la Belle qu’on est lundi, celle-ci acquerrait en fait une inadmissible evidence, c’est-à-dire une information qui peut justifier que ses degrés de croyance s’écartent des chances objectives. Un exemple plus clair est celui d’une boule de cristal infaillible qui prédit qu’une pièce donnée va tomber sur pile. Tout agent ayant cette prédiction en tête est certain que la pièce va tomber sur pile : une telle information sur le futur disqualifie les probabilités habituellement associées à l’objet « pièce de monnaie équilibrée ». Autre exemple extrême : la Belle qui apprend qu’on est mardi devient tout simplement certaine que la pièce est tombée sur pile, donc ne fait plus coïncider probabilités épistémique et ontologique. Puisque « on est mardi » est une information inadmissible, alors l’information concurrente « on est lundi » l’est aussi et justifie que la Belle puisse se désolidariser de la probabilité 1/2 en adoptant à la place 2/3. Bradley explique encore que l’annonce « on est lundi » ressemble à une prédiction : jusqu’alors incapable de se repérer dans le temps, un agent qui soudain apprend la date ou l’heure apprend en même temps, en quelque sorte, des informations sur le futur, puisqu’il découvre quelles sont, parmi toutes les positions temporelles possibles, ou plutôt parmi toutes les parties temporelles de l’agent (tous les individuals-at-times au sens lewisien), celle qui est actuelle, celles qui appartiennent au passé et celles qui appartiennent à l’avenir.

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29 Bradley fait de notre pouvoir de localisation dans le temps une prescience insoupçonnée. Mais sa critique échoue. Le protocole de l’expérience de la Belle interdit les réveils-face-mardi, donc la série des réveils-mardi produite par répétition de l’expérience est tout entière une succession de réveils-pile. Cela signifie que les chances objectives d’avoir un réveil-face-mardi sont nulles. Apprendre qu’on est mardi rend la Belle certaine qu’elle est dans un réveil-pile, justement parce qu’elle calque ses degrés de croyance sur des chances objectives. Bradley se focalise sur la pièce de monnaie comme si elle représentait tout le dispositif aléatoire : c’est une première erreur. Il oublie que les événements produits sont des réveils et, à tort, ne considère comme chances que la propension de la pièce à tomber sur un côté plutôt que sur l’autre. Sa deuxième erreur consiste à croire que les inadmissible evidences se rencontrent facilement dans la vie d’un agent rationnel. En réalité, le demiste dénonce des écarts entre probabilités épistémiques et ontologiques dont il a lui-même forcé l’existence, soit en occultant des éléments du dispositif aléatoire, soit en brodant une histoire où le surnaturel est roi (la boule de cristal).

30 P(Face|Lundi) = 1/2 : voilà la seule estimation acceptable. Certaines analyses, certaines remarques du demisme traditionnel sont sans doute éclairantes, mais l’estimation 2/3 (sachant lundi) est à rejeter. Le tiérisme, qu’il soit fréquentiste ou bayésien, n’est pourtant pas forcément vainqueur...

3 L’analogie avec le problème de Monty Hall

31 Quelques auteurs ont abordé la question des similitudes entre le Monty Hall et la Belle au bois dormant. Halpern [Halpern 2004] et Jenkins [Jenkins 2005] considèrent que les tiéristes font la même erreur que les défenseurs du 1/2 − 1/2 pour le Monty Hall. Weatherson ne partage pas ces analyses et estime que la trop grande différence entre les deux problèmes ne permet pas de trancher [Weatherson 2011]. Il est vrai que le Monty Hall n’est pas un problème d’auto-localisation et qu’il ne fait plus peur à nombre d’adeptes des mathématiques récréatives, mais il fait partie, avec la Belle, de ces paradoxes qui entraînent les philosophes insatisfaits par l’inférence bayésienne sur des voies polémiques, à la recherche de lois de dynamique doxastique originales.

32 Dans le jeu de Monty Hall interviennent un présentateur et un candidat placé devant trois portes fermées (A, B et C) ; derrière l’une d’elles se trouve une voiture et derrière chacune des deux autres une chèvre. Le candidat doit d’abord désigner une porte (par exemple, A). Puis le présentateur ouvre une porte qu’il sait n’être ni celle qui cache la voiture, ni celle choisie par le candidat (ce sera, mettons, C). Celui-ci a alors le droit ou bien d’ouvrir la porte qu’il a choisie initialement, ou bien d’ouvrir la troisième porte (B) : il gagnera le lot correspondant. Que doit-il faire et quelles sont ses chances de gagner la voiture ? Deux réponses rapides et intuitives s’opposent : • Après ouverture de la porte par le présentateur, il reste deux portes qui ont autant de chances l’une que l’autre de cacher la voiture. On aurait donc 1/2 de chances de gagner sans changer, 1/2 de chances en changeant. • Mais si l’on ne change pas de porte, on gagne si on avait fait le bon choix au départ ; or ce choix avait une chance sur trois d’être bon. Il y aurait donc 1/3 de chances de gagner sans changer contre 2/3 en changeant.

33 La réponse 2/3 en changeant fait aujourd’hui consensus. La réponse 1/2 correspond aux chances de gagner en sélectionnant au hasard une des deux portes restantes et pas en

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changeant de porte rationnellement. Les défenseurs du 1/2 reprochaient aux avocats du 2/3 de considérer que l’ouverture d’une mauvaise porte laisse inchangée la probabilité que la porte initialement choisie soit la bonne. Il est effectivement légitime de se demander pourquoi l’ouverture d’une porte ne modifie la probabilité que d’une des deux autres. En particulier, il est évident que si deux portes étaient ouvertes, la probabilité de gagner deviendrait 0 ou 1.

34 Comprendre que le candidat est certain, juste avant l’intervention du présentateur, qu’une chèvre va être « découverte » derrière une des portes B et C (mais pas A) est essentiel pour faire disparaître le paradoxe. Le dimanche soir, la Belle est elle aussi dans un tel état de certitude, sûre d’être réveillée durant l’expérience mais aussi d’être réveillée lundi. Un réveil mardi constituerait la seule surprise. Ce qui est commun aux problèmes de Monty Hall et de la Belle, c’est d’abord cette situation d’un agent qui sait en partie ce qui va se passer et qui refuse de croire que la réalisation des événements prévus puisse d’une quelconque façon le renseigner sur l’état d’un objet donné (l’orientation d’une pièce de monnaie ou l’éventuelle présence d’un gain derrière une porte choisie).

35 Dans son analyse du problème de la Belle, Cozic accepte la partie du raisonnement demiste lewisien qui conclut la réponse 1/2 à la question principale, mais aussi le raisonnement du tiériste Elga qui conclut la réponse 1/2 à la question subsidiaire du lundi [Cozic 2007]. Chacune de ces réponses est intuitive, et pourtant leur égalité rebute les bayésiens persuadés que l’annonce « on est lundi » confirme face. Cozic étudie alors les concepts d’imaging et de mise à jour, qu’il distingue de la conditionalisation et de la révision. Il montre en particulier que l’imaging, règle de dynamique des croyances esquissée sans optimisme par Lewis en 1976, pourrait, en invitant la Belle à conserver lundi la probabilité de face, réconcilier demistes et tiéristes autour d’un compromis double-demiste. Pour autant, l’imaging, que Cozic lie étroitement à la mise à jour (variation de l’intensité des croyances d’un sujet qui apprend que son environnement a changé), ne correspondrait pas précisément à la règle que la Belle devrait suivre.

36 L’habitude de la conditionalisation rend l’imaging suspect. Pourtant, si l’on regarde le problème de Monty Hall en groupant les portes B et C, les seules que le présentateur est susceptible d’ouvrir, la solution 2/3 − 1/3 est celle que l’on obtiendrait par application de l’imaging ; la conditionalisation classique y parvient aussi mais en suscitant l’étonnement et en contribuant à l’effet paradoxal. Certes, nous sommes dans un contexte de révision des croyances, pas de mise à jour, mais l’imaging ne pourrait-il pas être aussi un outil de révision ?

37 Les schémas de la figure 1 montrent que la réponse 1/2 − 1/2 résulte d’une conditionalisation modifiant jusqu’aux branches principales de l’arbre (nous l’appellerons désormais conditionalisation profonde ou C.P.), alors que la réponse 2/3 − 1/3 correspond à un imaging qui, par définition, n’affecte que les branches secondaires sœurs.

38 Les positions tiériste, demiste et double-demiste peuvent être présentées sous forme d’arbres probabilisés similaires à ceux du Monty Hall. Dans un premier temps, le protocole peut être décrit par la figure 2. La Belle sait qu’une pièce est lancée le dimanche soir, que si face sort, elle sera réveillée lundi (RL) avec probabilité 1, que si pile sort, elle sera réveillée lundi avec probabilité 1 et mardi (RM) avec probabilité 1. Aussi, à chaque expérience, la probabilité d’être réveillée est 1, la probabilité d’être réveillée lundi est 1 et la probabilité d’être réveillée mardi est 1/2. Au réveil, la Belle

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doit cependant adapter ces valeurs car elle ne peut croire qu’au degré 1 qu’elle est réveillée lundi ou mardi. Le problème est de déterminer la manière correcte de ventiler au réveil les probabilités du dimanche soir, puis de répartir ces probabilités après l’annonce « on est lundi ».

Figure 1 – Les schémas du Monty Hall

Figure 2 – Le protocole de la Belle

39 • Un tiériste, conditionnellement au réveil, réajuste les probabilités face-pile et les probabilités RL et RM (si pile). En apprenant que c’est lundi, il modifie encore les probabilités face-pile et les probabilités RL et RM (si pile) [cf. Fig. 3].

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Figure 3 – La Belle tiériste

40 Au réveil, une Belle tiériste modifie ses croyances par conditionalisation profonde. Dès qu’elle sait que ce réveil a lieu lundi, elle utilise également la C.P.

41 • Un demiste, conditionnellement au réveil, ne modifie pas les probabilités face-pile mais uniquement les probabilités RL et RM (si pile). En apprenant que c’est lundi, il modifie les probabilités face-pile et à nouveau les probabilités RL et RM (si pile) [cf. Fig. 4].

Figure 4 – La Belle demiste

42 Au réveil, une Belle demiste modifie ses croyances par imaging . Puis, en apprenant que c’est lundi, elle utilise la C.P.

43 • Un double-demiste, conditionnellement au réveil, ne modifie pas les probabilités face- pile mais uniquement les probabilités RL et RM (si pile). En apprenant que c’est lundi, il ne modifie toujours pas les probabilités face-pile mais modifie à nouveau les probabilités RL et RM (si pile) [cf. Fig. 5].

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Figure 5 – La Belle double-demiste

44 Au réveil, une Belle double-demiste modifie ses croyances par imaging, règle qu’elle suit à nouveau dès qu’elle sait qu’on est lundi.

45 On peut donc considérer que le tiérisme applique une double C.P., le double-demisme un double imaging ; le demisme traditionnel, lunatique et décidément suspect, applique un imaging puis une C.P. L’imaging réunit les schémas résultant des raisonnements double-demistes et le schéma des raisonnements qui résolvent le Monty Hall, quand bien même certains de ces raisonnements, à l’origine, ne reconnaîtraient que la conditionalisation classique. Si l’on accepte les similitudes entre les deux paradoxes, si l’on tient la C.P. pour une règle inadaptée à leur situation commune, le double-demisme prend le dessus sur le tiérisme... qui n’a cependant pas dit son dernier mot.

4 La leçon des compagnons de la Belle

46 La variante suivante est au cœur d’un argument tiériste apprécié [Neal 2006, 15–17], [Stalnaker 2008, 63]. La Belle s’endort dimanche soir avec son Prince. Elle est réveillée, en compagnie du Prince avec lequel elle peut alors s’entretenir, selon le protocole de l’expérience originale (lundi si face, lundi et mardi si pile). Comme la Belle, le Prince est endormi à l’aide de la drogue à effet amnésique ; il ignore de quel côté est tombée la pièce et ne peut dater le jour de son réveil que si on lui donne l’information ; il connaît le protocole entier. La différence, c’est qu’il est réveillé lundi et mardi quel que soit le résultat du lancer de la pièce ; il peut donc arriver qu’il soit réveillé alors que la Belle reste endormie. Voici que le Prince se réveille et comprend que l’expérience est en cours. Respectueux du principe d’indifférence, il attribue la probabilité épistémique a priori 1/4 à chacune des quatre hypothèses centrées, exclusives et conjointement exhaustives : T1 : « Aujourd’hui est lundi et la pièce est tombée sur pile » T2 : « Aujourd’hui est mardi et la pièce est tombée sur pile » H1 : « Aujourd’hui est lundi et la pièce est tombée sur face » H2 : « Aujourd’hui est mardi et la pièce est tombée sur face ».

47 Il découvre alors que la Belle est aussi réveillée. Bien qu’il sût que cette situation

arriverait durant l’expérience, il reçoit une nouvelle information indexicale : ¬H2,

autrement dit T1 ∨ T2 ∨ H1. La probabilité de H2 est maintenant annulée et, par

conditionalisation équivalente à un partage de l’ancienne probabilité 1/4 de H2 entre les trois hypothèses restantes, le Prince doit maintenant attribuer à chacune des trois

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la probabilité 1/3, ne voyant pas pourquoi en favoriser une au détriment des autres. Par conséquent, il doit à présent croire au degré 1/3 que la pièce est tombée sur face.

48 Les demistes et certains double-demistes acceptent cette partie du raisonnement tiériste, mais ils soulignent, à la manière de leur critique d’une variante similaire décrite par le tiériste Dorr en 2002, que la Belle, contrairement au Prince, ne peut jamais avoir l’occasion d’apprendre que celui des deux sujets rationnels qui dans cette expérience peut ne pas être réveillé mardi, à savoir elle-même, est ou n’est pas réveillé, puisqu’un tel apprentissage nécessite la conscience, l’état de veille, donc l’événement dont la réalisation ou la non-réalisation, justement, est à apprendre. En d’autres termes, selon le demisme, comprendre que la construction mentale « j’apprends que je suis réveillé » est aussi absurde que « j’apprends que je dors », c’est comprendre que la dynamique des croyances de la Belle engagée dans l’expérience est différente de celle des croyances du Prince.

49 Poursuivons le raisonnement tiériste. La Belle et son Prince peuvent à présent discuter et surtout échanger leurs estimations de la probabilité de face. Si la Belle est tiériste, les estimations se rejoignent, ce qui ne produit chez elle aucun questionnement particulier. Si elle est demiste, les estimations divergent : ce désaccord de deux agents rationnels n’est pas rare, mais il serait bien étrange qu’ils ne parviennent pas à faire concorder leurs estimations après avoir mis en commun leurs connaissances. Et si la demoiselle hésite entre 1/2 et 1/3 ? Ne doit-elle pas repenser au raisonnement tiériste du Prince, ne peut-elle pas adopter sa conclusion ? Si nous admettons que la Belle doit calquer son degré de croyance sur celui de son compagnon, nous pouvons encore objecter que la présence de celui-ci modifie de façon significative l’expérience originale. Alors, par variations successives, plaçons-nous progressivement dans les conditions de l’expérience originale, d’abord en supposant que le couple est séparé par un rideau, puis que le Prince se situe dans une chambre isolée sans aucun moyen de dialoguer avec sa bien-aimée ; finalement, examinons le cas où le compagnon n’est plus du tout là et où la Belle ne peut que l’imaginer et comprendre le raisonnement tiériste qu’il pourrait tenir. À quel moment doit-elle cesser de croire au degré 1/3 en l’obtention de face ? Jamais, répondront les convaincus.

50 La variante du Prince pourrait mettre le double-demisme en difficulté : l’idée d’une divergence persistante de deux estimations probabilistes rationnelles portant sur la même croyance au même moment ne semble pas supportable. Pourtant, nous devrions avoir de sérieux doutes. Le Prince serait plus informé, plus savant que la Belle, ses probabilités à lui feraient autorité ? Contestable, étant donné l’asymétrie subtile de leurs cheminements mentaux. Toutefois, mettre en relation la Belle avec un compagnon est une bonne idée ; l’argument est perfectible s’il repose sur une variante plus ingénieuse que nous allons à présent introduire et analyser.

La variante des Quatre Belles

51 Quatre Belles participent à une expérience dont elles connaissent toutes les règles. Le dimanche soir, elles s’endorment. On tire alors au sort une des quatre, équitablement : elle est ainsi désignée pour être réveillée lundi et seulement lundi. Puis on tire au sort une Belle parmi les trois restantes : elle est désignée pour être réveillée mardi et seulement mardi. Les deux sujets restants seront réveillés lundi et mardi. Le lundi, on laisse dormir profondément la Belle désignée pour ne pas être réveillée ce jour-là, on

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réveille les trois autres, on les réunit pour un entretien, puis on les rendort après leur avoir administré une drogue qui leur fait oublier tout ce qui s’est passé dans la journée. Le mardi, on réveille les trois Belles qui doivent être réveillées ce jour-là, on les réunit pour un entretien, on les rendort avec la même drogue. Les Belles n’ont aucun moyen de savoir si on est lundi ou mardi, ni de connaître le résultat précis des tirages au sort, sauf si on les renseigne dans la conversation (néanmoins, elles savent évidemment que la Belle qui dort a été désignée par le sort). Le mercredi, on les réveille toutes les quatre et l’expérience est terminée.

52 Dans ce scénario, en quelque sorte, quatre expériences de Belle au bois dormant sont menées simultanément et imbriquées de telle façon que, chaque jour, exactement trois Belles sont réveillées et peuvent facilement communiquer entre elles. Les mondes centrés dont la Belle au bois dormant faisait originellement correspondre ses hypothèses semblent rendus, par impossible, physiquement accessibles et non plus seulement mentalement accessibles, ils sont comme réalisés en mêmes monde, lieu et temps pour permettre à leurs trois ambassadrices, conscientes de l’absence d’une quatrième restée inconsciente, de se rencontrer.

53 Suivons Aurore, une des Belles engagées dans l’expérience. Elle se réveille avec deux autres Belles, toutes trois sont incapables de se repérer dans le temps au jour près ; la quatrième Belle continue à dormir. À quel degré Aurore doit-elle croire qu’elle est une « désignée », c’est-à-dire que le hasard, au premier ou au second tirage, l’a désignée pour qu’elle ne soit réveillée qu’un jour sur les deux jours de l’expérience, autrement dit juste aujourd’hui ?

54 Raisonnons d’abord ainsi : deux Belles sur quatre sont désignées, et comme les tirages sont équitables, Aurore avait une chance sur deux, dimanche soir, d’être désignée. Il semble que ce soit différent maintenant, car Aurore comprend comme tout le monde que la Belle qui est en train de dormir est une des deux désignées. Il reste trois Belles, une seule d’entre elles est une désignée, il n’y a aucune raison apparente de ne pas partager les probabilités équitablement : Aurore devrait donc croire au degré 1/3 qu’elle est une désignée. Un argument fréquentiste naïf supporte cette probabilité : si l’expérience des Quatre Belles était répétée de très nombreuses fois, un réveil d’Aurore sur trois serait un réveil dans une expérience où Aurore est désignée.

55 Changeons de cap et soyons bayésiens quelque temps. Intuitionnons et raisonnons à la manière de Lewis dans la première partie de son analyse en faveur de la réponse 1/2 à la question principale posée à la Belle au bois dormant, partie louée par tous les demistes et double-demistes. Demandons-nous ce qu’Aurore a appris entre dimanche soir et maintenant. Elle est réveillée et l’expérience est en cours ? Mais elle savait déjà dimanche qu’elle devait être réveillée durant l’expérience. Aucun bayésien ne voit comment utiliser cette information pour modifier un degré de croyance. Elle a appris que c’est Lucie, et non ses deux autres amies Estelle et Norah, qui est désignée pour rester endormie aujourd’hui ? Mais, là encore, elle savait d’avance qu’elle serait réveillée en compagnie de deux autres Belles et que le protocole, qui exige qu’une des deux désignées reste endormie, allait du coup lui révéler, non pas une désignée quelconque, mais une désignée qui ne peut en aucun cas être elle-même, Aurore ! Que cette désignée restée endormie soit Lucie, Estelle ou bien Norah, cela ne fait aucune différence et n’a aucune incidence sur les croyances. Par conséquent, Aurore n’apprend rien de pertinent. Ses certitudes du dimanche sont celles d’aujourd’hui, à ceci près, par exemple, qu’elle sait aujourd’hui que Lucie dort, et non Estelle ou Norah, ce qui,

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répétons-le, est sans importance. Les demistes comme Bradley feraient remarquer qu’une Belle qui reste endormie toute la journée ne peut pas avoir conscience qu’elle est une désignée. Aurore n’a jamais l’occasion de se dire, au moment de son ou ses réveils, qu’elle est certainement une désignée, mais elle a toujours l’occasion de se croire (sans aucune certitude) désignée. Donc elle ne peut pas être surprise, elle ne peut pas apprendre. Elle croyait dimanche au degré 1/2 qu’elle serait désignée ; maintenant que l’expérience est en cours, elle doit croire au même degré qu’elle est une désignée.

56 Notre réflexion sur la situation d’Aurore à son réveil nous a permis d’envisager deux raisonnements aux conclusions différentes : le premier ne peut être tenu que par les tiéristes (de l’énigme originale de la Belle au bois dormant) et il mène à la probabilité 1/3 ; le second ne peut être tenu que par les demistes (et les double-demistes) et il mène à la probabilité 1/2. En outre, gageons que si le second raisonnement, d’une façon ou d’une autre, s’avérait inconsistant, ou si sa conclusion avait des effets embarrassants, le demisme et le double-demisme en pâtiraient parce que, manifestement, ce raisonnement subjectiviste n’est ni plus ni moins que le raisonnement fondateur de tous les courants demistes, mais appliqué à une variation du problème original. Celle-ci, par certains aspects, s’éloigne davantage du problème original que ne le faisait la variante du Prince, mais ce n’est pas grave du tout tant que les demistes se reconnaissent.

57 Poursuivons l’analyse. Pour Aurore, continuer à croire au degré 1/2 qu’elle est une désignée a une conséquence fâcheuse : étant donné qu’une et une seule des trois Belles éveillées est une désignée et qu’Aurore n’a pas de raison de penser qu’Estelle a plus (ou moins) de chances que Norah d’en être une, Aurore doit estimer à seulement (1 − 1/2)/ 2 = 1/4 la probabilité que chacune de ses deux amies éveillées soit une désignée. En d’autres termes, le demisme oblige un sujet (Aurore) à faire de lui-même une sorte d’élu qui, au milieu des gens réveillés, aurait plus de chances qu’un autre d’être celui qui ne sera réveillé qu’une fois pendant l’expérience ! Si ses deux compagnons de veille raisonnent comme lui, ils vont tirer des conclusions identiques mais centrées sur eux- mêmes. Au final, chacun des trois demistes croit au degré 1/2 qu’il est un désigné et réduit ce degré à 1/4 pour chacun de ses compagnons. « J’ai plus de chances que les autres d’être un désigné », pense l’un. « J’ai plus de chances que les autres d’être un désigné », pense un autre. Mais ces « Je » ne représentent pas la même personne.

58 Soyons encore plus démonstratifs : Aurore a maintenant l’occasion de discuter avec Estelle et lui affirme : « Tu as une chance sur quatre d’être une désignée. » Estelle répond : « Moi ? Une chance sur deux plutôt ! » Ainsi, les Belles ne peuvent qu’échanger des estimations contradictoires. Quand une probabilité subjective estimée ne peut pas être « interpersonnalisée », elle ne peut qu’être essentiellement personnelle, si intime et incommunicable qu’elle n’inspire plus confiance.

59 La grande force de la variante des Quatre Belles, c’est que l’étrangeté des conséquences de la position demiste confine à l’absurdité. L’aventure de la Belle et de son Prince ne provoquait pas un tel rejet des estimations conflictuelles. Au contraire, dans ce scénario, désaccords et contradictions avaient une excuse de taille : le protocole de l’expérience faisait en sorte qu’un agent établisse son propre espace de probabilité, à partir de données différentes des données du compagnon, et il faisait en sorte que le centrage de chaque univers probabilisé le rende plus résistant à la transformation raisonnée généralement observée lorsque deux agents partagent leurs informations pour affiner et harmoniser leurs croyances. La variante des Quatre Belles se distingue.

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En effet, les trois Belles réveillées ne participent pas seulement à une même expérience, elles sont aussi à égalité face au protocole, leurs états cognitifs et leurs croyances ne devraient pas présenter de différences significatives. Après avoir suivi strictement le même raisonnement demiste, comment peuvent-elles continuer à croire en privé à un certain degré alors que leurs voisines croient à un autre degré ? N’y a-t-il pas une incohérence au sein du (double-)demisme ? Le tiérisme, lui, ne semble pas manquer de cohésion dans la même situation, bien au contraire, et les trois Belles devraient se sentir obligées d’abandonner le demisme si elles veulent croire ensemble au même degré que chacune d’elles est une désignée.

60 Première objection : le protocole offre aux Belles désignées une journée entière de repos, donc leur réserve un sort différent de celui des Belles non désignées qui sont réveillées une fois de plus. Nous répondons : et alors ? Les Belles ignorent le sort qui leur est réservé, c’est justement là-dessus qu’elles s’interrogent, alors que, dans la variante du Prince, les deux agents connaissent leurs rôles. Le protocole de notre variante fait en sorte que les Belles considèrent au même moment les mêmes possibilités centrées exclusives et conjointement exhaustives : « Je suis une désignée et on est lundi », « Je suis une désignée et on est mardi », « Je ne suis pas une désignée et on est lundi » et « Je ne suis pas une désignée et on est mardi ». Que ces quatre hypothèses soient équiprobables ou pas, à chacune d’elles chaque Belle réveillée doit accorder une crédibilité, la même que celle estimée par ses deux amies éveillées. C’est en ce sens que nous affirmons que les Belles sont à égalité face au protocole.

61 Deuxième objection : eh bien, justement ! même demistes, les Belles ne sont pas vraiment en conflit, elles s’entendent parfaitement sur la façon de probabiliser les quatre possibilités centrées mentionnées ci-dessus, et c’est seulement lorsque le pronom « je » est remplacé par « Aurore » ou un autre prénom que leur tranquillité prend fin. Nous répondons : si leur tranquillité prend fin, il y a bien conflit derrière une paix apparente, et c’est toute la subtilité de la variante ! Les quatre possibilités ne sont pas essentiellement centrées, dans le sens où, bien que chaque Belle s’interroge sur la partie temporelle d’elle-même qui est actuelle (« Moi-lundi ? Moi-mardi ? »), elle sait très bien qui est « moi », qui est « je ». D’une part, Aurore sait qu’elle est Aurore et il en va de même pour ses amies ; d’autre part, « je » ne représente aucune autre Belle que celle qui prononce le mot. Même si ces agents rationnels égaux devant le protocole évaluent exactement de la même manière la probabilité de « Je suis une désignée », ce « je » ne fait pas référence à la même personne si c’est Estelle et non plus Aurore qui le formule. Seule une Belle sur les trois en état de veille est une désignée : leur désaccord est inévitable si une probabilité autre que 1/3 est attribuée à l’hypothèse « Je suis une désignée ». Accord et désaccord semblent essentiellement liés aux estimations ; contrairement au protocole-piège du scénario du Prince, l’innocent protocole des Quatre Belles dirige les agents dans des réflexions centrées identiques qui devraient immédiatement les mettre d’accord, même sur des croyances décentrées. Les agents ne vivent pas dans la pure relativité : « je » est un individu concret identifié, « je » est à absolutiser et à nommer dès que possible, sinon « je » s’estime élu au milieu d’« eux », les autres, refuse un dialogue qu’il considère comme conflictuel, garde des croyances à jamais personnelles. Les (double-)demistes sont-ils des « je » extrémistes ?

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5 Discussion

62 Les éléments de réflexion développés dans cet article sont de trois ordres. La question posée par l’arbitrage fréquentiste est essentielle : la possibilité de mesurer par une fréquence observée la probabilité recherchée serait un argument statistique déterminant, et la réconciliation du subjectivisme et de l’objectivisme permettrait de résoudre le paradoxe. Malheureusement, la répétition de l’expérience de la Belle ne produit pas l’effet escompté. La fréquence de réveils-face, clairement égale à 1/3, ne mesure qu’un ersatz de probabilité. La spécificité de la suite de réveils pose en réalité la question également non résolue de la définition du concept de suite aléatoire. Néanmoins, la suite de réveils-lundi réunit les solutions tiériste et double-demiste et condamne pratiquement le demisme classique.

63 Nous avons ensuite discuté l’analogie avec le Monty Hall, problème dont la solution est tenue pour acquise par la plupart des bayésiens et des fréquentistes. La résolution du Monty Hall par imaging a pourtant une pertinence, et des similitudes entre les deux paradoxes nous invitent à examiner la Belle également sous l’angle de l’imaging et de la conditionalisation profonde. Ces deux règles de répartition des probabilités caractérisent, l’une le double-demisme, l’autre le tiérisme, ce qui laisserait là encore le demisme classique sur le carreau. Prolonger l’analogie avec le Monty Hall avantage cependant le double-demisme. Un tel argument n’est pas irréprochable : imaging et C.P. étant peu théorisés et éprouvés, il est difficile de savoir s’ils fondent une analogie qui surmonte les différences objectives entre les deux paradoxes.

64 Enfin, l’étude d’un scénario retors est approfondie par la construction de variantes de plus en plus fines. La symétrie des « compagnons » et la confrontation des estimations personnelles et interpersonnelles font des Quatre Belles une variation aboutie, qui semble donner raison au tiérisme. Pourtant, la nécessité d’une convergence des estimations personnelles cohérentes en une probabilité interpersonnelle n’est pas totalement établie, des zones d’ombre persistent. Les Belles sont-elles en mesure de partager leurs connaissances au point qu’elles deviennent communes au sens lewisien ? Pour niveler les estimations des compagnons, ne faut-il pas élever en principe la thèse selon laquelle, à épistémès égales, deux agents rationnels ne peuvent être « d’accord pour être en désaccord » ? Nous reconnaissons la doctrine d’Harsanyi, séduisante mais pas consensuelle. Par exemple, Binmore, en rappelant l’hypothèse du « petit monde » de Savage, écrit : Je préfère défendre la théorie d’Harsanyi comme étant une hypothèse de travail plutôt qu’un principe philosophique. [Binmore 1992, 470]

65 Les nombreuses pistes de résolution du paradoxe favorisent tantôt une école, tantôt une autre. Telle une ombre insaisissable, la Belle au bois dormant se rit de chaque nouvel éclairage et nous démontre son actuelle inaccessibilité. Ce miroir de vérité nous renvoie notre incapacité à donner des définitions univoques et à fonder les sciences sur d’indestructibles évidences. Comprenons que ce n’est pas pour nous humilier et nous décourager, c’est au contraire pour nous alerter, nous affermir et, en définitive, nous faire progresser.

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BIBLIOGRAPHIE

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NOTES

1. Tierciste serait plus juste, mais le mot tiériste l’emporte dans les rares articles en français et dans les correspondances des chercheurs. 2. [Delabre 2008] propose une vue d’ensemble du débat plus détaillée.

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RÉSUMÉS

Dans cet article sont commentées trois tentatives de résolution de la Belle au bois dormant, la célèbre énigme d'auto-localisation qui engendre un paradoxe probabiliste troublant : l'arbitrage fréquentiste propose une lecture ontologique des probabilités lorsque l'approche bayésienne atteint une limite ; l'analogie avec le Monty Hall s'efforce de penser de nouvelles règles de révision doxastique communes aux deux problèmes ; enfin, la leçon des compagnons encourage le partage et l'harmonisation d'estimations probabilistes entre agents rationnels. Chacun des trois arguments est rappelé brièvement, puis certaines parties sont examinées plus attentivement, critiquées ou au contraire appuyées par des idées neuves, telles que la variante des Quatre Belles.

In this paper, three pathways are discussed so as to resolve the famous Sleeping Beauty problem, a self-location puzzle that causes a troubling probabilistic paradox: the frequentist arbitration proposes an ontological reading of probabilities when the Bayesian approach reaches a limit;the analogy with the Monty Hall game tries to conceive new doxastic revision rules that apply to both problems; finally, the lesson of the companions encourages the sharing and harmonization of probabilistic estimates between rational agents. All three arguments are briefly recalled, then some portions are scrutinized, criticized or on the contrary supported by new ideas like the Four Beauties variation.

AUTEURS

LAURENT DELABRE Université Paris 1 Panthéon-Sorbonne. UMR 8590 -- IHPST (France)

LÉO GERVILLE-RÉACHE Université de Bordeaux UMR 5251 -- Institut de Mathématiques de Bordeaux (France)

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